Donald Trump has said he is considering a Polish request to establish a permanent US military base in Poland as a bulwark against Russia, noting that Warsaw was prepared to pay “billions” for the facility.

Trump spoke on the matter at a joint press conference on Tuesday with his Polish counterpart, Andrzej Duda, who had come to White House to press his government’s arguments for a base, which he jokily suggested could be called “Fort Trump”.

Trump said he agreed with Duda’s arguments that Russian actions, especially the seizure of parts of Georgia and Ukraine, warranted a tough response.

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

The US currently supplies most of the troops, about 900, for a rotating Nato battalion in Poland as part of the alliance response to Russian intervention in Ukraine and Moscow’s muscle-flexing along its western borders involving large-scale military exercises.

Warsaw has been pushing for a larger US presence and a permanent base on Polish soil.

“We believe that the presence of the United States is a guarantor of security in our part of Europe,” Duda said. “I was smiling when I was talking to Mr President. I said that I would very much like for us to set up a permanent American base in Poland, which we would call Fort Trump. I firmly believe that this is possible. I am convinced that such a decision lies both in the Polish interest and in the interest of the United States.”

Trump declared himself open to the idea, stressing that Poland would pay for the facility.

“The president offered us much more than $2bn to do this, so we are looking at it,” Trump told reporters. “We’re looking at it from the standpoint of number one, military protection, for both countries, and also cost. A term you don’t hear too often.”

Trump is reported to have ordered a review of costs of basing US troops in Germany, against a backdrop of poor relations with Germany. Diplomats in Washington says he is furious with German chancellor Angela Merkel about car exports and Berlin’s cooperation in the planned Nord Stream 2 gas pipeline connecting Russia and western Europe. Trump has also pressured Merkel to buy US liquefied natural gas (LNG), but there is limited demand for it in Germany for cost reasons.

Duda stressed Polish willingness to buy LNG and his government’s scepticism over the Nord Stream 2 pipeline which he said would deepen European energy dependence on Russia. He also pointed out that Poland was buying US Patriot missiles for its anti-ballistic defences.