Abe comes to power as tensions simmer with China over ownership of disputed islands in the East China Sea, said he will work to improve the "trust-based relationships" necessary for a strategic defense partnership with the United States, Kyoto said.
"We will strategically conduct diplomacy ... and above all else, we must rebuild the trust-based relationships in the Japan-U.S. alliance," Abe said.
Abe, 58, also announced his Cabinet choices during his first news conference since returning to power following Wednesday's elections.
Abe's Liberal Democratic Party returns him to power for the first time since his year-long stint from September 2006 to September 2007. He is the first politician to make a comeback for the position in 64 years.
The success of the LDP in recent elections represents a transfer of power from the Democratic Party of Japan, which had been in power for more than three years.
Abe said Taro Aso, who was prime minister in 2008-09, will serve as deputy prime minister, finance minister and state minister for financial services.
Akira Amari was appointed to a new Cabinet position of economic revitalization minister. The Financial Times said Amari developed Abe's economic strategy.
The Times said the Cabinet announcements come after Abe's campaign focused on reviving the economy.