U.S. Defense Secretary Lloyd Austin visited Ukraine on Monday, in a show of Washington's support for Kyiv just two weeks ahead of a U.S. presidential election that is casting uncertainty over the future of Western support.

Austin's trip, his fourth and likely final visit as President Joe Biden's Pentagon chief, will include in-depth discussions about U.S. efforts to help Kyiv shore up its defences as Moscow's forces advance in the east.

But it is not expected to include a new U.S. agreement to some of Ukrainian President Volodymyr Zelenskiy's biggest requests, like lifting U.S. restrictions on using U.S.-supplied weapons to hit targets far beyond Ukraine's borders.

As Biden's administration winds down, Austin signalled continuity in U.S. support.

"We're going to continue to support Ukraine in its efforts to defend its sovereign territory," Austin told reporters travelling with him to Ukraine.

"We've watched this fight evolve over time. And each time that it does evolve, we have risen to the occasion to meet (Ukraine's) needs to make sure that they were effective on the battlefield."

His visit comes ahead of the Nov. 5 U.S. presidential vote, in which former President Donald Trump, the Republican candidate, is seeking re-election in a close race against Vice President Kamala Harris, the Democratic candidate.

Trump has signalled he would be more reluctant than Biden to continue to support Ukraine, which could deprive Kyiv of its biggest military and financial backer.

Austin played down concerns, saying he saw support for Ukraine from both Republicans and Democrats in Congress.

"I've seen bipartisan support for Ukraine over the last 2-1/2 years, and I fully expect that we'll continue to see the bipartisan support from Congress," he said.

The retired four star general has been one of Ukraine's staunchest advocates, building a coalition of dozens of nations who have supplied Kyiv with weaponry that has helped it deal heavy blows to Moscow's forces.

One U.S. defences official, speaking on condition of anonymity, said Russia had suffered 600,000 casualties of killed and wounded troops in Ukraine so far, with September being its heaviest month of fatalities and injuries.

But Russian President Vladimir Putin seems content to invest more and more forces in a costly advance in eastern Ukraine's Donbas region, which he says he wants to gain full control over.

In recent weeks, Russia has surrounded towns in the Donetsk region and then slowly constricted them until Ukrainian units are forced to withdraw.

"It's a very tough fight and it's a tough slog," Austin said.

'Victory plan'

Meanwhile, Kyiv has been seeking to keep its war in focus in the West, even as the expanding conflicts in the Middle East grab the international spotlight.

Zelenskiy last met Austin in Brussels on Thursday at the NATO headquarters, where he pitched his "victory plan."

The Ukrainian leader received pledges of continued support but no endorsement from key allies of his call for an immediate NATO-membership invitation.

Asked about Zelenskiy's victory plan at NATO headquarters on Friday, Austin responded: "It's not my position to evaluate publicly his plan."

Kyiv may need to start making tough decisions about how to employ its stretched fighting forces, including whether it will hold onto territory Kyiv seized in Russia's Kursk region in a surprise offensive this summer, experts say.

The Kursk offensive caught Austin and the U.S. government off-guard. Kyiv hoped it would wrest the battlefield initiative from Russia including by diverting Moscow's forces from the eastern front.

But Putin has remained focused on seizing the key city of Pokrovsk in eastern Ukraine, which is an important logistics hub for Kyiv's war effort.

Even with billions of dollars worth of U.S. military support, including the provision of F-16 fighter jets, Abrams tanks and more, Ukraine faces a tough fight ahead.

Although its invasion of Ukraine has inflicted blows to Russia's economy, made it more isolated diplomatically and battered its military, Russia "is not ready to call it quits," a senior U.S. defence official said.

"And so that does place a steep burden on the Ukrainians," the official said, speaking on condition of anonymity.