The House on Tuesday approved a nearly $40 billion package of humanitarian and military aid to Ukraine, the latest tranche of relief to the country the U.S. is aggressively backing in its fight against Russia.

The bill, which was finalized earlier Tuesday and includes nearly $7 billion more funding than requested by the Biden administration, was approved in a 368-57 vote, with all Democrats backing the bill and all opposition coming from Republicans.

With the vote, Congress has now directed more than $50 billion to support Ukraine in the war with Russia. The House voted 36-169 on March 9 on a $13.6 billion package for Ukraine and other key European allies.

The Senate is expected to vote on the measure in the coming days.

The package includes $6 billion to help train, equip and support the Ukrainian armed forces, and more than $9 billion to replenish the U.S. stockpiles of military equipment and ammunition in the U.S. and abroad that have been tapped to re-arm Ukraine.

The measure would also help fund and support U.S. troops stationed in Europe and the operation of a Patriot air defense missile system in Europe, and it includes more than $900 million to support Ukranian refugees with housing, counseling and English language classes, as well as helping process and screen those traveling to the United States.

Additionally, the bill directs the inspector general of the Defense Department to provide a written report to the House and Senate defense committees reviewing the Ukraine program spending within 120 days of the law's enactment.

-ABC News' Ben Siegel

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

Mariupol has not yet fallen, despite Russia's demands that Ukrainian troops defending the besieged Ukrainian port city surrender, according to Ukrainian Prime Minister Denys Shmyhal.

"There [are] still our military forces, our soldiers, so they will fight until the end," Shmyhal told ABC News' George Stephanopoulos in an exclusive interview Sunday on "This Week."

Mariupol is a strategic city for Moscow because it would allow Russian forces in the south to connect with troops in eastern Ukraine's contested Donbas region. It would also give Moscow a key port.

Although Mariupol remains under the Ukrainian government's control, Shmyhal said the city's residents are suffering.

"They have no water, no food, no heat, no electricity," he said. "They ask all of our partners to support and help stop this humanitarian catastrophe."

-ABC News' Monica Dunn