The three-day visit comes after Russia, which strongly opposes the project, announced it was suspending its participation in a key European arms control treaty.
Talks at the White House between Kaczynski and Bush on July 16 are expected to pick up negotiations that began in Poland in June over the missile-defense shield.
The United States wants to place 10 interceptors in Poland and a radar station in the Czech Republic.
Washington insists the missile-defense system is aimed at countering the threat of a nuclear terror attack from "rogue" threats that include Iran and North Korea.
But Russia says it views the U.S. plan as a threat to its national security and has responded energetically, including with an offer to allow a facility in Azerbaijan to be used for the missile-defense effort.
On July 14, the Kremlin announced that Russian President Vladimir Putin signed a decree suspending Russia's participation in the Conventional Forces in Europe (CFE) Treaty.
Russian Deputy Foreign Minister Sergei Kislyak said the move was connected to NATO's eastward expansion and what he said were violations of the CFE Treaty by the NATO alliance.
Kislyak also said Moscow remained open to dialogue.
"I would like to stress that we are not closing the door to dialogue," Kislyak said. "We presented proposals to our partners to find a solution. And we are still waiting for a constructive response."
The CFE Treaty, originally signed by Warsaw Pact and NATO member states in 1990, and amended in 1999, limits the amount of troops and conventional weaponry that signatory countries can deploy on their territory. But the United States and other NATO members have refused to ratify the amended version of the treaty, saying Russia must first withdraw troops from Moldova and Georgia.
NATO, the United States, and individual European states expressed disappointment at Russia's fresh decision to suspend participation.
"The CFE is one of the foundations of the situation which was created after the end of the Cold War," Poland's Deputy Foreign Minister Witold Waszczykowski told Reuters. "And we of course would like to keep this treaty, of course with some amendments, with some amendments, with some modifications which were discussed and were implemented some years ago. But of course we wouldn't like to pull out from the treaty, [and] we wouldn't like Russia to pull out from this treaty."
View From Warsaw
Poland's participation in the U.S.-led multinational force in Iraq is also expected to figure on the agenda of Kaczynski's visit.
Poland has been a staunch U.S. ally since the launch of the U.S.-led invasion of Iraq in early 2003, and currently has about 900 soldiers in Iraq. But President Kaczynski has recently signaled an unwillingness to leave Polish troops in Iraq beyond the end of this year.
During his U.S. visit, the Polish president is also scheduled to honor late U.S. President Ronald Reagan with one of Poland's highest distinctions, presenting his widow Nancy Reagan with the Order of the White Eagle in Los Angeles on July 17.
AN RFE/RL VIDEO PRESENTATION: The Czech Republic responds to the U.S. missile-defense proposal.