WASHINGTON—The U.S. will be unable to continue providing weapons and equipment to Ukraine if Congress doesn’t approve additional funding by the end of the year, the White House said on Monday, warning of devastating consequences on the battlefield if lawmakers fail to act.

“Cutting off the flow of U.S. weapons and equipment will kneecap Ukraine on the battlefield, not only putting at risk the gains Ukraine has made, but increasing the likelihood of Russian military victories,” Shalanda Young, the director of the White House Office of Management and Budget, wrote in a letter to House Speaker Mike Johnson (R., La.).

The letter marks one of the White House’s most forceful pleas for congressional action to date and lays out in detail the consequences of inaction. “There is no magical pot of funding available to meet this moment. We are out of money—and nearly out of time,” Young wrote.

Without additional money, the U.S. won’t have the necessary resources to procure additional weapons and equipment for Ukraine or to provide resources from existing U.S. military stockpiles, Young said.

Federal agencies have spent all or nearly all of the $111 billion in supplemental funding approved by Congress to support Ukraine. As of mid-November, the Defense Department had used 97% of the money it received and the State Department had spent 100% of the military assistance-related funding it received, according to the letter. Other pots of aid are similarly depleted.

Pentagon officials said they had issued contracts for all of the $10.5 billion in available funds for new weapons for Ukraine, and have only a little left to replenish U.S. stocks after spending $16.8 billion on missile defense systems, artillery shells, tanks and other equipment.

“It’s fumes,” said Pentagon acquisition chief Bill LaPlante when asked what was left for Ukraine. LaPlante, speaking on the sidelines of the Reagan National Defense Forum in Southern California, said there were already standing requests for further Ukraine support amounting to four times more than the available funding.

Officials in the U.S. and Europe are increasingly worried as the war in Ukraine nears the end of its second year, fearing that Russian President Vladimir Putin will be able to outlast the political will of Western countries to continue aiding Ukraine.

Biden in October outlined a $106 billion proposed aid package for Ukraine, Israel and Taiwan. The package requested about $60 billion to fund the Ukraine war effort and replenish U.S. weapon stocks.

Congress is debating how to proceed, with Republicans calling for more border security measures and changes in immigration policy in exchange for approving the additional money. A possible vote on such a measure could come this week in the Senate.

The spotlight would then shift to Johnson, who has publicly and repeatedly called Ukraine aid a critical priority for the House in recent weeks, despite voting against additional security assistance for Kyiv earlier this year before he became speaker.

House Republicans have faced growing pressure to reject Ukraine aid, as voters in their congressional districts have soured on the effort. A recent AP-NORC poll found that 59% of Republicans believe the U.S. is spending too much on Ukraine. Congress has approved more than $100 billion to help Kyiv since Russia invaded.

In a closed-door lunch this past week, Johnson warned Senate Republicans that the House GOP can’t pass a large aid package that combines funds for the border, Ukraine and Israel, the approach sought by Biden and favored by Senate leaders. He told the senators he wants to break up the package and vote on Ukraine aid and border policy separately from Israel aid.

Young used Monday’s letter to make the case to skeptical Republicans in Congress that funding will offer direct benefits to the U.S. by boosting the American defense industry. Sixty-percent of the money that has been approved so far by Congress has supported the U.S. defense industrial base or boosted Defense Department and intelligence operations, she wrote.

“That has improved our own military readiness since DOD is buying new equipment to replace what we are sending Ukraine, jump-starting and expanding production lines, and is supporting good-paying jobs in dozens of states across the country,” she wrote, adding that Biden’s recent request for additional money would funnel tens of billions of additional dollars to the U.S. defense industry.

—Lindsay Wise and Doug Cameron contributed to this article.

Write to Andrew Restuccia at andrew.restuccia@wsj.com, Doug Cameron at Doug.Cameron@wsj.com and Michelle Hackman at michelle.hackman@wsj.com