"And we want to invest further, we want to modernize Polish armed forces", Duda said during a White House news conference with President Trump.
"I invite you to post more American military troops in Poland", Duda said, calling a U.S. presence a "guarantor of security".
Duda, during his first trip to the White House since Trump took office, pledged to cover $2 billion of the costs of a new US military base in Poland and name it after Trump, citing a need for increased defense amid "very strong militarization" and "aggressive behaviors" by Russian Federation in recent years.
Poland "likes the idea very much", according to Trump, who has been looking at the prospect of putting a permanent military base in Poland "very seriously".
"I would like to see a permanent American base in Poland".
The White House has said that trade, the military and security issues will be part of the conversation with the nation of 38 million that has close ties to the United States.
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Mr Trump, who seemed enticed by the offer, said he deemed the security of Poland "almost as important" to him as it is to the Polish president. "And we have the greatest strength in the world, especially now", Trump said. We want to implement more projects.
However, all the USA forces shuffle in and out of Poland and there is no permanent American base in the country.
Later in the event, Trump and Duda took questions from the audience.
"If they're willing to do that, it's something we will certainly talk about", he added.
Warsaw could offer up to US$2 billion in funding for a United States military base, according to a Polish Defense Ministry proposal reported by Polish media.
Poland and other Eastern European countries have been lobbying the United States to increase the number of troops on the continent as they worry about combating an increasingly aggressive Russian Federation.
"There is a whole range of arguments in favor of the fact that the presence of the U.S. armed forces in this area is absolutely justified", Duda said. Equipment of the previous United States unit stationed there, has, however, "remained in place" for reasons unexplained, according to Russian military. Ben Hodges, a well-known Russian Federation hawk, has argued that stationing the American military in Poland permanently would be seen as unnecessarily provocative by fellow members of North Atlantic Treaty Organisation and divide the alliance.
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