The State Department is urging Congress to quickly move on passing additional funding for Ukraine, calling the aid "vital" and warning the administration's other means of financing military support were quickly running out.

"Our assistance to Ukraine has been just as we promised: massive," State Department spokesperson Ned Price said during his daily briefing Tuesday. "We have provided $4.5 billion worth of security assistance to Ukraine since the start of this administration, some $3.8 billion worth of security assistance since the invasion began. These are supplies -- weapons -- precisely what Ukraine needs to defend itself."

But, he said, maintaining that support depends on lawmakers fulfilling the White House’s request for another $40 billion in funding.

"The fact, however, is that right now, our coffers in terms of drawdown funding -- they're dwindling," he said. "We now have less than $100 million left and we will exhaust those funds within the next week."

Price said the new tranche of funding would "help our Ukrainian partners and also our NATO allies do precisely what we feel it is imperative that they be positioned to do at this moment."

Pressed on whether the administration had a limit in mind when it came to sending lethal aid to Ukraine, Price said the focus was on fulfilling its promises to "provide Ukraine with the security assistance it needs to defend itself" and ensuring "our allies -- especially our allies on the eastern flank -- had what they needed to deter and potentially even respond to Russian aggression."

-ABC News' Shannon Crawford

Amid a three-year vacancy and with Ukraine in the grips of a brutal war, the U.S. Senate took its first major step towards confirming an American ambassador to Ukraine on Tuesday with a hearing in its Foreign Relations Committee for President Joe Biden's nominee, Bridget Brink.

Brink -- a veteran diplomat with 25 years of experience and the current U.S. ambassador to Slovakia -- acknowledged the great difficulties that would come with the post but said it would be the "honor of a lifetime."

"We face the biggest threat to peace and security in Europe in decades," she said during her opening statements. "If confirmed, I pledge to work with you to continue our commitment to a sovereign, democratic and independent Ukraine -- free to choose its own future."

Brink has bipartisan support and her path to confirmation appears to be a smooth one, though Sen. Jim Risch (R-Idaho), the ranking member of the committee, foretold "a lot scrutiny from Washington" when it comes to moving the U.S. embassy back to Kyiv and "helping to shepherd U.S. military, humanitarian and financial aid in the right places."

"I think it's really important for us to be there in person and present," Brink responded when questioned on plans to reopen the embassy in Kyiv. "I don't know exactly how fast we will be able to do this process, but I know we are trying to do it as fast as possible and it is certainly my hope and plan, if confirmed, to be able to start my mission in Kyiv."

She later added: "It's necessary for us to be there on the ground."

The nominee was also asked about the need for the aid package currently working its way through Congress.

"It is incredibly important that the supplemental move fast," Brink said. "The needs are large."

Brink also promised to work to assist Ukraine in holding Russia accountable for alleged war crimes.

"We are going to use every tool at our disposal," she said. "I can tell you it's a personal priority of mine."

-ABC News' Shannon Crawford

The House will vote on a new roughly $40 billion Ukraine aid package Tuesday night, House Speaker Nancy Pelosi announced.

The request includes funding for "critically needed resources, including military aid, support for the Ukrainian economy, and humanitarian assistance for food security to address the worldwide hunger crisis."

The White House had initially requested $33 billion in assistance for Ukraine, but congressional leaders decided to tack on an additional $7 billion for more military and humanitarian assistance.

"This package, which builds on the robust support already secured by Congress, will be pivotal in helping Ukraine defend not only its nation but democracy for the world. Time is of the essence – and we cannot afford to wait," Pelosi said in a letter to colleagues. "With this aid package, America sends a resounding message to the world of our unwavering determination to stand with the courageous people of Ukraine until victory is won."

The bill is expected to pass in the House, after which it would head to the Senate.

-ABC News' Mariam Khan

President Joe Biden will host House Speaker Nancy Pelosi and other members of Congress in the Situation Room on Tuesday afternoon to discuss the lawmakers' recent trip to Ukraine, according to White House press secretary Jen Psaki.

Biden previously spoke with Pelosi over the phone about her trip but wanted a more thorough discussion in person, Psaki said.

Expected to attend are: Rep. Jim McGovern, D-Mass.; Rep. Gregory Meeks, D-NY; Rep. Adam Schiff, D-Calif.; Rep. Barbara Lee, D-Calif.; Rep. Bill Keating, D-Mass.; and Rep. Jason Crow, D-Colo.

-ABC News' Ben Gittleson and Mariam Khan

Jalina Porter, the State Department's deputy spokesperson, is responding to the Russian attack at a Ukraine train station that killed at least 50, saying, "We can no longer be surprised by the Kremlin's repugnant disregard for human life."

Five children were among those killed when Russian rockets struck the station in Kramatorsk in Donetsk Oblast on Friday morning, according to Ukraine's state-owned railway company. At least 100 people were injured, according to Donetsk Oblast Gov. Pavlo Kyrylenko.

Russia has denied involvement in the attack, which occurred as "thousands" of civilians fleeing the Russian invasion were at the train station waiting to be taken to "safer regions of Ukraine," according to Kyrylenko.

"Civilians are killed when they stay in their homes, and they're killed when they try to leave," Porter said. "Actions like these demonstrate why Russia did not belong on the U.N. Human Rights Council, and they also reinforce the U.S. assessment that members of Russian forces are committing war crimes in Ukraine."

Porter declined to say if the department considers the train station attack a war crime, saying, "Assessing individual criminal liability in specific cases is the responsibility of courts, as well as other investigatory bodies. But as the secretary, Secretary [of State Antony] Blinken, has said, 'Those responsible for war crimes and other atrocities committed in Ukraine will be held to account.'"

-ABC News' Conor Finnegan