Abe is expected to reaffirm the two nation's security alliance and cooperation in dealing with North Korea, the Kyodo news agency reported.
"I would like to have a solid and irreplaceable Japan-U.S. alliance as the cornerstone of Japan's security ... and build a relationship with President Bush in which we can discuss everything frankly," Abe said to reporters prior to leaving Tokyo.
Abe said one of his goals is to have the United States confirm it will cooperate with Japan concerning the issue of North Korea's past abductions of Japanese nationals.
"I want to move toward its resolution with an iron will," he said.
Abe also is expected to meet with congressional leaders from both the Republican and Democratic parties, followed by visits to a U.S. Navy hospital and Arlington Cemetery.
Abe also will stop in the Middle East following his visit to the United States. He said he wants to build a "multilayered'' relationship with Mideast countries by building on issues such as energy, the environment and culture, Kyodo said.