At a meeting in the Oval Office, Bush called the missile-defense plan a "symbol of our desire to work for peace and security."
Kaczynski sought to reassure Russia that the program is not aimed at undercutting Moscow.
"It is aimed at defense of our democracies against the countries who might have or already do have nuclear weapons or weapons of mass destruction," the Polish leader said. "So it is really a defense instrument."
Washington says the planned system would protect most of the continent from long-range missile strikes from Iran or rogue regimes. The U.S. wants to place 10 interceptors in Poland and a radar station in the Czech Republic.
Bush said it would protect Europe from threats that "may emanate from parts of the world where leaders don't particularly care for our way of life and are in the process of trying to develop serious weapons of mass destruction."
Russia has voiced outrage at the plans and warned it could spark a new arms race. Russian officials have also threatened to retarget its missiles toward Europe to counter the proposed missile defense installations.
Russian President Vladimir Putin said on Saturday his country would suspend its compliance with the Conventional Forces in Europe Treaty after 150 days.
In their talks, Bush thanked Kaczynski for Poland's help in Afghanistan and Iraq. Poland has 900 troops in Iraq and is still deciding whether to bring its soldiers home from Iraq by year's end, as planned.
"War is never popular," Bush said.
During his three-day U.S. visit, Kaczynski is also scheduled to honor the late President Reagan with one of Poland's highest distinctions, presenting his widow Nancy with the Order of the White Eagle in Los Angeles on Tuesday.