Russia launched new attacks on Ukraine on Sunday, using missiles and Iranian-kamikaze drones to strike Odessa and the Zaporizhzhia region, as protesters in several Russian cities demonstrated against the war effort and a new mass conscription.

Russia's drive to mobilize 300,000 new fighters and to stage illegal "referendums" in four occupied regions of Ukraine mark a sharp escalation by President Vladimir Putin, as he tries to hold the line despite multiple failures in his ongoing invasion, including a major retreat in the Kharkiv region earlier this month.

The efforts, amid warnings from Russian officials that Moscow could use nuclear weapons to defend illegally annexed regions, appear designed to shake Ukraine's resolve and to undermine Western military support for Kyiv. But Ukraine and its allies insist the moves are evidence that Russia is panicking - and that it can be beaten on the battlefield.

"He knows that he's losing the war," Ukrainian President Volodymyr Zelensky said of Putin during an interview with CBS's "Face the Nation" on Sunday. "They admitted that their army is not able to fight with Ukraine anymore. . . . They did not expect the resistance that they received from us."

Within Russia, there were signs that the public was losing patience with the mobilization and the war in Ukraine.

Scuffles broke out Sunday in Makhachkala, the capital of Dagestan, where screaming women struggled with police and tried to prevent them from dragging male protesters to police vans. It was a rare sign of dissent that underscored the dangers of regional unrest over the mobilization.

Earlier Sunday in Dagestan, an impoverished southern region that has borne a disproportionate share of military casualties in Ukraine, furious residents blocked a highway to protest the mobilization of 110 men from Endirey village, including some who had recently returned from the war, independent local media reported.

In eastern Siberia, meanwhile, several hundred women rallied Sunday in the city of Yakutsk, chanting "No to war" before police broke up the rally and arrested participants, according to local media outlets and activist groups.

And in Moscow, demonstrators also took to the streets Sunday to protest reports of the conscription of some who were elderly, sick, disabled or otherwise unfit or exempt from military service.

The backlash underscored the potential that Putin's military mobilization could trigger opposition within the large segment of the Russian population that passively supports the war - although the Kremlin may be banking on anger waning after the initial shock and fear following the announcement wear off.

National security adviser Jake Sullivan said Sunday that the demonstrations against mobilization in Russia were entirely predictable and suggest that Putin's losses in Ukraine have backed him into a corner.

"He knew that as soon as he ordered mobilization, there would be some upheaval in the country, and we're seeing the images and scenes of that right now," Sullivan said on NBC's "Meet the Press." He added that the referendums in Ukraine are "a sign that he is struggling very badly in Ukraine."

But, Sullivan added, "that doesn't mean that the danger is over. It is very much real and still with us."

Putin is expected to address both houses of parliament on Friday, state media reported. He is likely to endorse the annexation of the regions after the expected official announcement that the regions voted in favor of joining Russia. Russia has a long history of flawed and fraudulent elections, but the Kremlin will not be satisfied with anything less than a massive "yes" vote, according to analysts.

This weekend, armed soldiers accompanied officials going house-to-house, observing people filling in ballots. The referendums, which U.S. officials have labeled a "sham," have met none of the basic criteria for democratic voting, and they are illegal under international law.

Zelensky predicted Sunday that Putin would use the questionable results as a pretense to rally his population behind the invasion.

It is unclear what other nations will recognize Russia's land grab. Even Moscow's close ally Serbia on Sunday rejected the referendums. Its foreign minister, Nikola Selakovic, told journalists that they violated the principles of territorial integrity, sovereignty and the inviolability of borders, according to Serbian cable network Nova.rs and Russian state-owned RIA Novosti.

Ukraine and its allies have insisted that Russia's annexation will change nothing on the battlefield. They stress that they remain committed to helping Ukraine reclaim territory seized by Russian forces despite Putin threatening last week to "use all available means" to defend territory it claims as Russian, including nuclear weapons.

Sullivan said on NBC on Sunday that "there will be catastrophic consequences for Russia" if Putin uses nuclear weapons, and that "the United States will respond decisively." He declined to specify publicly what those consequences would be but noted U.S. officials have been more explicit in private warnings to their Russian counterparts.

In the meantime, Russia pummeled new targets in Ukraine this weekend, firing missiles into Zaporizhzhia and hitting an administrative building in Odessa with Iranian-made drones. Ukrainian officials said no one was injured in the Odessa strikes, but video images of a large explosion in the city center underscored the potential of such weapons to cause destruction and terror in civilian areas.

The General Staff of Ukrainian Armed Forces reported attacks on at least 35 settlements in the east and south of the country over the weekend, which led to at least three deaths and 19 injuries. According to Russian state media, a Ukrainian strike on a hotel in Kherson killed a pro-Kremlin former Ukrainian lawmaker, Oleksiy Zhuravko.

Ukrainian fighters are attempting to reclaim Kherson via a counteroffensive, as they did with territories in the Kharkiv region earlier this month. It is also one of the places Russia plans to annex via referendums ending Tuesday.

Andrei Turchak, the head of Putin's United Russia Party, predicted that "the Kherson region will return to the big Russian family," during a visit there Sunday as he portrayed the results of the five-day referendum as a foregone conclusion.

Elsewhere, however, influential members of Russia's political class joined the voices criticizing the Kremlin over the recently launched mobilization.

Prominent Kremlin propagandist Margarita Simonyan, editor in chief of RT and one of the loudest cheerleaders of the war, published an astonishing Twitter thread Saturday listing cases of people wrongly mobilized. They included a 63-year-old with diabetes and cerebral ischemia, a 35-year-old with a spinal fracture and artificial vertebrate, and sole caregivers to disabled people.

Vyacheslav Volodin, speaker of the State Duma, or lower house of parliament, also acknowledged the problems in comments Sunday on Telegram, calling on people to report violations to authorities. Vyacheslav Gladkov, the governor of Russia's Belgorod region, just over the border from Ukraine's Kharkiv regions, said he had received many complaints, including 75 cases of men wrongly mobilized that were overturned after his intervention.

Russia's initial "partial mobilization" was supposed to be limited to men in the military reserves with military experience. A different picture has emerged since, however, with many of those called up having never previously served.

The sense of panic deepened when two independent Russian media outlets reported that new travel restrictions would kick in Wednesday barring men of military age from leaving without permission from military enlistment offices. Several Russian regions have already restricted reservists from leaving.

As officials went into damage control mode, two regional leaders announced that planeloads of men who had been erroneously conscripted were returning home.

But many Russians have already left the country to avoid the mobilization. Social media was flooded in recent days with reports of Russian cars queuing to cross the border with Finland, and airline tickets from Moscow to destinations like Istanbul and Yerevan, Armenia, skyrocketing in price and selling out.

Alexei, a 36-year-old Russian who was previously exempted from conscription because of heart problems, said Sunday in a phone interview that he had fled to Astana, Kazakhstan, because he feared being called up.

"There are already so many examples of old and unfit men and students receiving summons," he said. "It's not that I am a coward or anything, but nobody is attacking my motherland. On the contrary, my motherland is an aggressor and I don't want to be part of this aggression and obviously I do not want to die."

Stories like Alexei's appear to have alarmed government leaders close to Putin.

Valentina Matviyenko, a close Putin ally who is the speaker of the upper house of parliament, the Federation Council, warned Sunday that partial mobilization must be handled "without a single mistake." She further stated in comments on social media, that the cases of people being mobilized who clearly should not have been were "unacceptable."