President Trump said the force would be taken from America's 52,000-strong contingent in Germany, and include drones and other military hardware.
He fell short, however, of committing to a permanent US base in the country.
It comes after offers from Warsaw to spend $2bn (£1.57bn) on building one.
The base may be called Fort Trump, President Duda quipped during his visit to the White House on Wednesday.
President Trump said America was "very interested" in the idea, but was reluctant to commit to a permanent facility - something that would likely prompt a response by Russia.
"I don't talk about permanence or not permanence," he told reporters, adding that the base "would certainly be a statement".
The visit - Mr Duda's second in less than a year - celebrated the 20th anniversary of Poland's membership in Nato, and the 30th anniversary of communism's downfall in the country.
Speaking to reporters, Mr Duda thanked Mr Trump for his "extreme kindness towards Poland and perfect understanding of Polish matters".
After leaving Washington, the Polish president is scheduled to visit Texas, Nevada and California for talks on energy and technology.