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, BBC reports.
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".