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.
For the past year the Warsaw government has been lobbying the Americans to establish a permanent military base in Poland to host up to a division (several thousand) US troops.
The idea was quickly dubbed “Fort Trump”. But there were problems.
Who would pay? Up to $2bn was offered by Warsaw, but this would only cover the initial establishment of the base.
Where would the troops come from? Moving them lock stock and barrel from the US would be hugely costly; shifting some from Germany or Italy might damage alliance cohesion.
Above all, a permanent base might breach the 1997 agreement between Nato and Russia.
What’s happened is a fudge. Fewer troops than requested, and again on a rotational basis. This is seen by US commanders as boosting readiness.
But these rotational troops will help to develop Poland’s military infrastructure to be able to receive much greater numbers of soldiers if necessary in the future.
What have the US and Poland agreed to?
The two leaders have signed a joint declaration affirming the countries’ co-operation on defence.
The agreement includes provisions for Poland to provide “basing and infrastructure for 1,000 American troops”, who would be temporarily stationed on a rotational basis.
When later questioned reporters, however, Mr Trump said “they’re talking about 2,000 troops”.
Speaking to the BBC, an official from the US Department of Defense was unable to confirm how many personnel would be sent to Poland under the new agreement.
It is also unclear who would shoulder the cost of the latest US deployment.
Around 5,000 troops already rotate in and out of Poland. This is part of a 2016 Nato agreement, made in response to Moscow’s annexation of Crimea from Ukraine in 2014.
In a separate deal, Poland has ordered 32 F-35 fighter jets, which are made in the US by Lockheed Martin.
Shortly before the press conference, in an unusual display, two F-35 planes flew over the White House to show off their moves.
Mr Trump hailed them as “the world’s greatest fighter jet – most advanced plane, probably, anywhere in the world beyond fighter jet; most advanced plane”.