By Jeff Mason, Patricia Zengerle and Richard Cowan

WASHINGTON (Reuters) -The United States is running out of time and money to help Ukraine fight its war against Russia, White House officials warned on Monday.

Democratic President Joe Biden's administration in October asked Congress for nearly $106 billion to fund ambitious plans for Ukraine, Israel and U.S. border security but Republicans who control the House with a slim majority rejected the package.

White House budget director Shalanda Young, in a letter to Mike Johnson, the Republican speaker of the House of Representatives, and other congressional leaders, said cutting off funding and a flow of weapons would "kneecap Ukraine on the battlefield" and increase the likelihood of Russian victories.

"I want to be clear: without congressional action, by the end of the year we will run out of resources to procure more weapons and equipment for Ukraine and to provide equipment from U.S. military stocks," Young wrote in the letter released by the White House. "There is no magical pot of funding available to meet this moment. We are out of money - and nearly out of time."

Congress has approved more than $110 billion for Ukraine since Russia's February 2022 invasion but it has not approved any funds since Republicans took over the House from Democrats in January.

Senate Majority Leader Chuck Schumer said on Monday night that Ukraine President Volodomyr Zelenskiy has been invited to address senators via secure video on Tuesday as part of a classified briefing to hear what is at stake.

The closed briefing for senators is scheduled for 3 p.m. EST on Tuesday and will feature U.S. national security officials.

The House and Senate last approved $45 billion in military, financial and humanitarian aid for Ukraine as part of a broader annual spending bill passed in December 2022.

Bipartisan talks about U.S. border security funding, which Republicans want to link to Ukraine funding, have sputtered in the Democrat-controlled Senate, several sources said on Monday.

Republicans have proposed significant changes as large numbers of immigrants arrive at the southern border with Mexico that Democrats argue would virtually shut down any asylum possibilities for migrants.

Johnson on social media said that Biden's administration has "failed to substantively address" Republican concerns about Ukraine strategy and said that any national security spending package must address U.S. border policies.

"We believe both issues can be agreed upon if Senate Democrats and the White House will negotiate reasonably," Johnson wrote on X, formerly called Twitter.

The House's failure to consider the White House request has raised concerns that funding for Kyiv might never be approved, especially after it passed a bill in November with funding for Israel but not Ukraine. The Senate's Democratic leaders rejected that bill.

Biden administration officials are expected to hold classified briefings for the House and Senate on Tuesday. The White House letter also went to Senate Majority Leader Chuck Schumer, a Democrat, Senate Republican leader Mitch McConnell and House Democratic leader Hakeem Jeffries.

'UP TO CONGRESS'

Biden, who is running for re-election in 2024, has rallied NATO allies to back Ukraine and said repeatedly that Russian President Vladimir Putin underestimated the West's resolve in supporting its neighbor against Russian aggression.

"Now it's up to Congress. Congress has to decide whether to continue to support the fight for freedom in Ukraine ... or whether Congress will ignore the lessons we've learned from history and let Putin prevail. It is that simple," Biden's national security adviser Jake Sullivan told reporters.

McConnell rejected the White House's strategy.

"Instead of engaging actively in the border security discussions required to complete a viable national security supplemental, the Biden administration has chosen to lecture - lecture - Congress with a brag reel of its supposed leadership in countering Putin in Europe," he said in remarks on the Senate floor.

Young said U.S. allies had stepped up their support for Ukraine, but that Washington's support could not be replaced.

By mid-November, the U.S. Defense Department had used 97% of $62.3 billion in supplemental funding it had received and the State Department had used all of the $4.7 billion in military assistance fund it had been allocated, she wrote.

Around $27.2 billion in economic aid money had been used up, as had $10 billion in humanitarian assistance.

Young said helping Ukraine "prevents larger conflict in the region that could involve NATO and put U.S. forces in harm's way and deters future aggression, making us all safer."

With a nod to important political swing states and Republican strongholds ahead of the 2024 presidential election, Young noted that funding could be used for contracts with companies in Alabama, Texas, Georgia, West Virginia, Wisconsin and Michigan.