Oil shipments from the energy-rich state to the world's second largest economy account for nine per cent of Japan's needs, with 12 per cent of its natural gas imports coming from Qatar.
On Monday, Abe met Sheikh Sabah al-Ahmad al-Sabah, the Kuwaiti emir, and Sheikh Nasser Mohammed al-Ahmed al-Sabah, his Kuwaiti counterpart, on the first visit to the Gulf Arab state by a Japanese premier.
He flew to Cairo on Wednesday to meet with Hosni Mubarak, the Egyptian president, on his way back to Tokyo.
Abe met leaders of Saudi Arabia and the United Arab Emirates (UAE) during the weekend.
He and King Abdullah agreed to forge "multi-layered" ties between Japan and Saudi Arabia, while the premier agreed with UAE leaders to launch a high-level dialogue to boost economic ties, pledging to speed up free trade talks.
Japan is increasingly concerned by potential threats to its energy supply.
It has virtually no oil or gas reserves of its own, and relies for more than 70 per cent of its oil supply on the four Gulf Arab states that Abe has been touring.
Early on Tuesday, Abe made the first visit by a Japanese leader to its personnel posted in Kuwait for an air force mission supporting US-led operations in Iraq.
Some 210 members of Japan's Air Self-Defence Force with three C130 transport airplanes have been deployed at the Gulf state's Ali Al-Salem Air Base west of Kuwait City.
The personnel are flying in goods and personnel between the base and Iraqi cities, including Baghdad, on behalf of the US-led coalition and United Nations despite Japan's withdrawal of ground troops last year.