KYIV — President Joe Biden’s Pentagon chief brought a message of continued U.S. support to Ukraine on Monday, even as Ukrainian troops struggle to hold back Russian forces and uncertainty hangs over Washington’s future role.

Defense Secretary Lloyd Austin, in his third wartime visit to Ukraine, held talks with President Volodymyr Zelensky and other government officials as the Biden administration seeks to help Ukraine chart the most effective course possible against Russia’s much larger military.

Ahead of the visit, however, Austin made clear that the United States was not ready to announce any changes to its refusal to permit Ukraine to use American-supplied arms to strike deep into Russia, a long-standing ask by Ukraine.

Austin’s visit was focused in part on Zelensky’s proposed “victory plan,” the Ukrainian leader’s new outline for what he says is necessary to recover Ukrainian territory but that has received a lukewarm response from his country’s backers in the West.

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The discussions come just two weeks before the American presidential election that could determine whether the United States continues its campaign of massive military support, which has enabled Ukraine’s scrappy military to keep Russia at bay since President Vladimir Putin’s 2022 invasion.

While Vice President Kamala Harris, if elected, would probably continue the flow of arms and funding to Ukraine, former president Donald Trump has promised to end the war swiftly, potentially on terms favorable to Moscow. That uncertainty compounds the challenges facing Ukrainian leaders as they grapple with Russian advances in eastern Ukraine and setbacks in sustaining their own offensive into Russia’s Kursk region.

Austin, speaking at the start of talks with Zelensky and his top aides, said the United States was committed to continuing its military support.

“The United States understands the stakes here,” Austin told the Ukrainian leader. “The outcome of Putin’s war of choice matters to us and to the entire world.”

Austin said the Biden administration would send Ukraine an additional $400 million worth of military equipment, including armored vehicles, antitank missiles and artillery shells, a donation that will be welcome but will not quench Ukrainian forces’ needs amid a prolonged, multi-front conflict with better-armed Russia.

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Like Biden’s other advisers, Austin has sought to emphasize the fact that Putin has failed to achieve the central goal of his invasion: to bring Ukraine fully under Kremlin control. Now, in the final months of Biden’s presidency, he and other administration officials are seeking to help Kyiv develop what they say must be a viable strategy that Ukraine can sustain with a finite supply of weapons and men.

“We really have been encouraging them and talking to them about how they can have a strategy that they apply specific military resources toward to have concentrated effect,” a senior defense official said, speaking on the condition of anonymity according to Pentagon ground rules.

U.S. officials say Ukraine is now in a better position on ammunition and other military supplies following lawmakers’ long-delayed approval of Biden’s supplemental funding package in April. They hope the morale boost provided by Kyiv’s surprise incursion into Kursk and an intensified push to mobilize needed troops at home can eventually propel Ukraine closer to a position of strength in eventual negotiations to end the war. They note that Russian casualties now total 600,000 dead and wounded and hit their highest rates of the war in September.

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But analysts say Ukraine remains outgunned in mortars, artillery and antitank munitions and must grapple with a dearth of air defense equipment and armored vehicles. It also faces a variety of personnel challenges, including difficulties in mobilizing and training adequate recruits and chronic undermanning of front-line units.

“Manpower is likely the most important factor that will determine the situation on the battlefield,” said Rob Lee, a senior fellow with the Foreign Policy Research Institute.

Ukrainian forces say improved tactics and superior numbers have enabled Russia to punch through their lines in places like the town of Vuhledar, which fell to Kremlin forces in recent weeks.

Russian forces have also secured recent advances in areas near Pokrovsk, Chasiv Yar and Kupyansk in the east, and they recovered some territory captured by Ukraine in Kursk.

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U.S. officials have declined to comment extensively on Zelensky’s victory plan, which the Ukrainian leader presented in NATO capitals in recent weeks. But U.S. officials say they see the proposal as falling short of what they had hoped to see: a blueprint laying out how military operations and objectives connect to the country’s larger strategic goals.

Officials note that they have already ruled out near-term support for two chief elements of the plan: an invitation to join NATO for Ukraine and permission to use U.S.-provided missiles to strike deep into Russia. Citing limited supplies of longer-range missiles and urging Ukraine to tap its homegrown drone industry, the Pentagon remains firmly opposed to the latter step.

American officials are now hoping to work with Ukraine to refine it into what they see as a more workable plan.

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Illustrating U.S. concerns about Ukraine’s strategy, American officials have also voiced concerns that the Kursk offensive could dilute its fighting power in the east, the Kremlin’s chief focus.

As Biden prepares to step down, his actions to counter Putin’s invasion — by spearheading a Western coalition to support Ukraine and catalyzing global actions to isolate Russia — will be a top item in his presidential legacy. Austin, a former Army general with extensive experience commanding troops in combat, likewise has made his mark by establishing an international grouping to catalyze and coordinate military supplies for Ukraine.

Ukraine must see to its immediate battlefield needs while fashioning a longer-term strategy despite not knowing whether its chief backer will continue or cease support.

Trump met with Zelensky last month in an encounter weighted with meaning given the former president’s admiring comments about Putin, the possibility he could curtail or end American arms supplies and his promise to broker an immediate end to the war if he is reelected.

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While Austin and other officials point out broad support among both U.S. parties for Ukraine, Biden’s months-long struggle to secure approval for this year’s $61 billion aid package, which put Ukrainian forces in a deep ammunition hole, points to the increasing difficulty that Harris or Trump might face in funneling American aid to Ukraine.

“Political wrangling in the U.S. and continued uncertainty over the support Ukraine can expect has made planning difficult,” said Michael Kofman, a senior fellow at the Carnegie Endowment for International Peace. “A common vision is more than a list of requirements. It needs to lay out how the approach and capabilities needed will attain the strategic objectives: in essence, a realistic theory of success.”