The two leaders, who spoke on the telephone this week for 10 minutes, are looking at a January summit in the United States, a report by The Japan Times newspaper said.
The security situation in the East China Sea and South China Sea has become tougher and Abe pledged Japan will "carry out its responsibilities" to maintain the power balance in Asia, an official who was in on the telephone discussion told the newspaper.
"I told (President Obama) that I'd like to strengthen the Japan-U.S. alliance, as this will help stabilize the Asian region," Abe said afterward.
His commitment to regional security comes after hard talk over China's claim to the Japanese-administered Senkaku Islands, known by Beijing as the Diaoyu Islands.
The official also said Abe confirmed Tokyo will cooperate closely with the United States in dealing with North Korea's recent firing of a long-range ballistic missile that reportedly put a satellite in orbit.
Abe is expected to take office Dec. 26 after winning an election that catapulted his Liberal Democratic Party back into power in the lower assembly, the House of Representatives.
The alliance of the Liberal Democratic Party and New Komeito Party won 325 seats in the 480-seat lower House, making Abe prime minister five years after resigning from office.
The LDP had ruled the country almost continuously from the party's establishment in 1955 to 2009 when it was ousted from power in the House of Representatives by the center-left Democratic Party of Japan.
This week the LDP trounced the DPJ led by Prime Minister Yoshihiko Noda, reducing it to 57 seats, down from 230 before the election.
The Japan Times report said neither leader specifically mentioned the Japan-China territorial dispute over the Senkaku Islands, although the issue remains a flashpoint between the Asian economic giants.
This month China flew a light aircraft low over the islands into airspace claimed by Japan -- the first such incident since Japan started monitoring the island and airspace in the late 1950s.
The event triggered diplomatic complaints by Tokyo as well as raised concern in Washington.
"It's important to avoid actions that raise tensions and to prevent miscalculations that could undermine peace, security and economic growth in the region," U.S. State Department spokesman Patrick Ventrell said.
Abe reiterated Japan's claim to the islands shortly after winning the election.
"We own and actively control the Senkaku Islands and on this point there is no room to negotiate," he said.
"In regard to this when Japanese companies and people are harmed in China, this is indeed against international rules. It is necessary to tell China and the international community that we won't tolerate this."
Abe's comments elicited harsh talk from Beijing.
A Chinese Foreign Ministry spokesperson said Japan-China relations were very important but warned Tokyo not to resume its militarily aggressive ways, a report by the state-run Xinhua news agency said.
"Whether Japan can face up to and repent the history of its aggression and follow the path of peaceful development has always had universal attention from its Asian neighbors and the international community," Foreign Ministry spokeswoman Hua Chunying said.
"There has been a trend of getting rid of the post-war system and denying peaceful development emerging in Japan in recent years. Asian countries and the international community need to be aware of this trend," she said.