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

At least one person -- a journalist -- was killed in a rocket attack on a residential building in Kyiv on Thursday evening, ABC News has learned.

Kyiv Mayor Vitali Kilitschko said Friday that rescuers had found the body of a victim amid the rubble.

Radio Liberty, a service of the U.S.-funded Radio Free Europe/Radio Liberty, reported that one of its employees, Vira Gyrych, was killed when a Russian missile hit her apartment in the Ukrainian capital on Thursday. Her body was found beneath the wreckage Friday morning, according to the report.

Gyrych had worked as a journalist and producer for Radio Liberty's Kyiv bureau since 2018. Prior to that, she worked for leading Ukrainian television channels, according to Radio Liberty.

"The editorial staff of Radio Liberty expresses its condolences to the family of Vira Gyrych and will remember her as a bright and kind person, a true professional," Radio Liberty said in its report.

Israeli Ambassador to Ukraine Michael Brodsky also confirmed Gyrych's death in a Twitter post, saying she was a former employee of the Israeli embassy in Kyiv.

Thursday's rocket attack came as United Nations Secretary-General Antonio Guterres visited Kyiv. Five Russian missiles flew into the city, according to Ukrainian President Volodymyr Zelenskyy. At least 10 people were injured, including four who were hospitalized, according to the Kyiv City Council.