Duda said he hoped the U.S. military presence in Poland would be enduring and would increase gradually.
Pressed on the point, Duda said: "There is no problem with democracy in Poland".
Trump said the United States has based tens of thousands of troops in Germany for a "long, long time" and that he probably would move a "certain number" of those personnel to Poland, "if we agree to do it".
President Trump is expected to make the announcement alongside Polish President Andrej Duda at a signing event at the White House.
US President Donald Trump welcomed Polish President Andrzej Duda to the White House on Wednesday. It includes just the addition of about 1,000 troops and a squadron of Reaper drones for intelligence purposes.
"This will be a very good and very fruitful day, because it will change both the shape of Polish-American military cooperation, as well as cooperation on energy issues", Krzysztof Szczerski, Duda's chief of staff, said on Wednesday.
"The United States intends to share information derived from this squadron's operations, as appropriate, in support of our defense objectives", the declaration, released by the White House on Wednesday, following a meeting between Polish President Andrzej Duda and his U.S. counterpart Donald Trump, read.
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Officials said Tuesday that the preliminary agreement avoids any permanent USA base or presence in the country and sticks instead to a rotational force.
Before the press conference, the two leaders will witness an F-35 Joint Strike Fighter aircraft flyover above the White House, in honor of Poland's intention to purchase F-35s for their own military, according to White House deputy press secretary Hogan Gidley. The service members will be added to an existing force of about 4,500 US troops that rotate in and out of Poland.
Asked by a reporter how he felt about Germany's decision to work with Russian Federation on the construction of the Nord Stream 2 pipeline, Trump said Germany was making a "tremendous mistake", and was making itself a "hostage" of the Kremlin.
The United States already has troops in Poland as part of a 2016 agreement with the North Atlantic Treaty Organisation military alliance in response to Moscow's annexation of Crimea from Poland's eastern neighbor Ukraine in 2014.
The eastern European nations have reached out to the USA and North Atlantic Treaty Organisation for greater protection, worrying that they might be the next target of Russia's military advance.
He also said he hopes Russian Federation "will treat Poland with respect".