WASHINGTON — Senior congressional Democrats and Republicans on Monday announced they had reached a deal on a bill that would punish Russia for invading Ukraine, as they seek to ban U.S. imports of Russian oil while further empowering President Biden to impose tariffs on the country’s products.

The announcement evinced the vast new flurry of legislative activity on Capitol Hill, even as lawmakers began to warn that the U.S. strategy threatened to further raise the cost of gas and other goods.

Unveiled by the top lawmakers overseeing tax and trade on Capitol Hill, the new, bipartisan agreement would limit Russian energy imports, suspend normal trade relations between the U.S. and the Kremlin and task the Biden administration to seek Russia’s suspension from the World Trade Organization. The trade penalties would also apply to Belarus, a key Russian ally in the Ukrainian conflict, according to the four members of Congress who crafted the deal.

“As Russia continues its unprovoked attack on the Ukrainian people, we have agreed on a legislative path forward to ban the import of energy products from Russia and to suspend normal trade relations with both Russia and Belarus,” they said in a joint, bipartisan statement.

“Taking these actions will send a clear message to [Russian President Vladimir] Putin that his war is unacceptable and the United States stands firmly with our NATO allies,” they continued, adding that Congress still needs to “do more.”

Signing the statement were Reps. Richard E. Neal, D-Mass., and Kevin Brady, R-Texas, the top lawmakers on the House Ways and Means Committee, and Sens. Ron Wyden, D-Ore., and Mike Crapo, R-Idaho, who oversee the Senate Finance Committee. The lawmakers did not share the full text of their plan.

The proposed package of punishments is only one prong of a broader congressional response to the rapidly worsening crisis in Ukraine. Democrats and Republicans also hope to approve $10 billion in humanitarian, military and economic assistance, a separate effort that they aim to append to a broader package to fund the federal government’s continued operations. A current spending agreement is set to expire at the end of the week, meaning inaction on the matter could shut down key agencies and programs.

In a letter to Democrats, sent early Monday, Senate Majority Leader Chuck Schumer, D-N.Y., offered an update on those talks: He said his party had made a “reasonable” offer to Republicans on a longer-term spending deal that accomplishes both tasks. Reflecting on its prospects, Schumer sounded an optimistic note, expressing his “hope that we will reach an agreement very soon.”

House Speaker Nancy Pelosi, D-Calif., similarly pledged swift action in her own note late Sunday, while teasing additional action to come, as the House is exploring “strong legislation that will further isolate Russia.”

The activity on Capitol Hill happened just days after Ukrainian President Volodymyr Zelensky delivered a direct plea to Congress. He asked for aid, including the provision of additional military equipment, which some lawmakers from both parties support. And Zelensky reiterated his calls for a no-fly zone, which Washington has rejected, as officials fear it could draw the U.S. into open conflict with another nuclear superpower.

The sum total of the new legislative efforts could come in addition to the punishing sanctions that the Biden administration has already imposed on the Kremlin and its wealthy, supportive elite. But the U.S. approach so far has not been without its consequences. The vast penalties levied by Washington and its allies against Russia have rattled economies globally, particularly in driving up the cost of gas. Americans have felt the sting at the pump acutely, as the national average price per gallon topped $4, nearing record highs recorded in 2008, according to AAA.

The potential for additional shocks prompted Democrats to stress this week that they also would forge ahead on a series of proposals that aim to ease Americans’ financial burdens.

“Our goal is to have the wages that have increased continue to go up and see costs go down so the average American has more money in their pocket,” Schumer told Democrats on Monday, noting party lawmakers would discuss some of the matters during a retreat scheduled this week.

The surge in gas prices has only compounded the country’s existing struggles with inflation, after federal data last month showed prices for rents, groceries, cars and other goods in January continued to jump at their fastest pace in roughly 40 years. With his party’s control of Congress on the line, Biden has committed to tackling inflation as a top priority, a promise made during his first-ever State of the Union address last week.

Some of the nascent legislative efforts — including now-bipartisan Senate talks to lower the price of insulin and promote competition — correspond with elements of Biden’s long-stalled economic agenda. Democrats have dusted off the ideas from the president’s original proposal, known as Build Back Better, which faltered last year amid divisions within their own party.

Pelosi, meanwhile, stressed on Sunday that Congress and the Biden administration are attuned to the possibility that conflict abroad could ratchet up prices at home — and ready to act in response. She pointed to the recent release of millions of barrels of oil in the country’s strategic reserve, a move meant to ease the supply crunch that had driven up costs at the pump.

“Let me be clear: the United States need not choose between our democratic values and our economic interests,” she wrote in her letter. “The administration and the Congress remain laser-focused on bringing down the higher energy costs for American families and our partners stemming from Putin’s invasion.”

The concerns about prices initially prompted the White House to raise a skeptical eye at the idea of blocking imports of Russian oil, though top aides to the president in recent days have expressed openness to the idea as pressure mounts on Capitol Hill to act. Imported Russian crude accounts for only a small portion of the U.S. oil market, but a U.S. ban could still have significant economic effects domestically — especially if other countries in Europe approve similar blockades.

“What we know is that, you know, from the U.S. economy, we don’t import a lot of Russian oil, but we are looking at options that we can take right now if we were to cut the U.S. consumption of Russian energy,” White House press secretary Jen Psaki said Friday. “But what’s really most important is that we maintain a steady supply of global energy.”

In the meantime, the immediate task facing lawmakers is to fund the government, which will run out of money once an existing short-term spending agreement expires after midnight Friday. Absent action, a slew of key federal agencies and programs are set to shutter, potentially imperiling Washington at a time when it is trying to manage a worsening crisis in Europe and a simmering pandemic in the United States.

Talks have progressed for weeks, and House leaders previously expressed hope they could vote on a package, known as an omnibus, as soon as Tuesday. But they face no shortage of obstacles in finalizing the deal at a time when the clock is ticking — and the stakes are high.

In recent days, Senate Republicans have threatened to slow down the Senate from acting ahead of the key fiscal deadline. One group has called for another vote on an attempt to defund federal policies requiring coronavirus vaccines and tests, despite public health guidance encouraging such rules. A second has sought a more thorough financial analysis of the spending bill, citing the effects of inflation.

The twin asks threaten to stall the narrowly divided Senate, which requires unanimity to speed up the debate process. It also could threaten prompt delivery of aid for Ukraine, even though Democrats and Republicans alike say it is necessary.

The Biden administration also has sought more than $22 billion to boost the country’s response to the coronavirus, arguing that more aid is needed to restock key public health programs in anticipation of a worsening pandemic. But Republicans have resisted the provision of this money, telling the White House last week they are not willing to support it unless they first see an accounting of the government’s existing spending.

Some GOP lawmakers have gone as far in talks as to demand Democrats supply financing for the new spending, including by repurposing billions of dollars set aside for cities and states to respond to the pandemic, according to two people familiar with the matter who requested anonymity to describe the conversations. The demand has raised the prospect that some or all of the aid may fall out of the deal as talks progress.

The Washington Post’s Steven Mufson, Mike DeBonis and Annie Linskey contributed to this report.