At a joint press conference with Polish President Andrzej Duda in the White House, Trump said Poland is offering to pay Washington at least $2 billion to help meet the costs of the base, which would likely irk an increasingly assertive Moscow.

"The president offered us much more than $2 billion to do this, so we are looking at it," Trump said.

"We are looking at it from the standpoint of, number one, military protection for both countries and also, cost.

"We're looking at it very seriously," the president said earlier. "If they're willing to do that (pay), it's something we will certainly talk about."

At the press conference, Duda said that NATO member Poland, which was long dominated by Russia and the Soviet Union, wants "a permanent American base in Poland."

He joked that the base could be called "Fort Trump."

Defense Secretary Jim Mattis praised Poland for taking a lead in increasing its military spending, but stressed that no decisions had been made regarding a permanent US troop presence.

"The questions are many," Mattis told Pentagon reporters.

"As you know, it's not just about a base. It's about training ranges, it's about maintenance facilities at the base, all these kinds of things, it's a host of details we've got to study alongside the Poles. So no decision's been made, we are studying it and we are working together on that."

Duda said Russian military expansion, starting with a takeover of rebel areas of neighboring Georgia and more recently the annexation of Ukraine's Black Sea Crimea region, was part of "constant violation of international law."

"There is a whole range of arguments in favor of the fact that the presence of the US armed forces in this area is absolutely justified," Duda said.

Trump -- accused by political opponents of having colluded in a shadowy Russian operation to aid his surprise 2016 election win against Democrat Hillary Clinton -- agreed with Duda's assessment.

"I think it's a very aggressive situation. I think Russia has acted aggressively," he said.

"They respect force. They respect strength as anyone does. And we have the greatest strength in the world, especially now."