“If they’re willing to do that, it’s something we will certainly talk about,” Trump said.

In May 2018, the Polish government offered to spend up to US$2 billion to establish a permanent US military presence in Poland.

A senior Polish government official said Warsaw would potentially be willing to spend even more over time or offer additional incentives to Washington.

US forces are already deployed to Poland on a rotational basis, part of an effort by the North Atlantic Treaty Organisation to step up defences on its eastern flank after Russia’s 2014 annexation of Crimea.

The United States does not currently operate any permanent military bases in Poland. In March, the United States and Poland said technical problems would delay completion of the Polish section of a US missile defence shield by two years to 2020.

While Poland has welcomed the American troop rotation as a deterrent against Russia, its government would like the Pentagon to establish a permanent divisional headquarters on Polish territory, as well as one other permanent brigade, according to the Polish official, who said his government hoped to get an answer from Washington by 2020.

Congress ordered the Pentagon to study the matter in this year’s defence policy bill, which Trump signed into law in August. The legislation instructs the defence secretary to submit a report to Congress no later than March 1, 2019, on the feasibility and advisability of permanently stationing US forces in Poland.

Germany has long been the primary base for American forces in Europe, with approximately 35,000 US service members stationed in the country.

Trump has been especially critical of Germany’s defence budget and trade surplus with the United States, leading to tensions with Chancellor Angela Merkel. At one point earlier this year, in a meeting with his advisers, Trump inquired about American troops stationed in Germany and asked about possibly removing them.

The Pentagon, however, has said the United States remains fully committed to Germany.

Standing beside Trump at the White House press conference, Duda was unapologetic in his praise for Trump’s leadership and business acumen, as the Polish president pitched a military expansion that could reignite an old fight with Moscow over the proximity of US forces to Russia.

“I’m hugely delighted with the presence of US armed forces in the Polish territory,” Duda said, inviting Trump to send more American troops to the nation.

Duda noted Polish purchases of American arms and said he wants to buy more. Trump smiled.

“I told Mr President about all the aspects connected with the permanent presence of the US armed forces in Poland,” Duda said. He said he had assured Trump that a permanent US base in Poland would not result in a newly heightened military stand-off with Russia in central and Eastern Europe, because he said that was already happening.

“It is the reality that we live in today,” Duda said.

Trump, who looked annoyed at times by Duda’s long answers, jumped in at one point to note that Poland has promised to pay “billions of dollars for a base.”

When a Polish reporter asked Trump about his own view of Russian behaviour in Europe, Trump did not hesitate to agree with Duda.

“I think it’s a very aggressive situation,” Trump said. “I think Russia has acted aggressively. They respect force. They respect strength, as anyone does, and we have the greatest strength in the world, especially now.”

Russia isn’t the only one opposed to the idea.

The former US Army commander in Europe, retired Lieutenant General Ben Hodges, a well-known Russia hawk, has argued that stationing the American military in Poland permanently would be seen as unnecessarily provocative by fellow members of Nato and divide the alliance.