The incoming Reagan administration got off to a good start with Japan this week when the president-elect agreed to keep Democrat Mike Mansfield as ambassador here.

Japanese officials took the news as a signal that Ronald Reagan wants to strengthen relations.

Prime Minister Senko Suzuki called the reappointment "a very good thing," and his top aide, chief Cabinet Secretary Kiichi Miyazawa, described Mansfield as a man who "understands" Japan.

Japanese newspapers reported today the Susumu Nikaido, chairman of the ruling Liberal Democratic Party's executive board, made the request late last year during a visit to Washington, where he met with Richard Allen, Reagan's top foreign-policy adviser.

The reports from Washington that Reagan would reappoint the 77-year-old former Senate majority leader were page-one news here.

Reagan called Mansfield about midnight Wednesday to ask him to remain in the post.

Mansfield readily accepted. Appointed by President Carter in 1977, he initially said he would not serve beyond Carter's term. But last fall he began throwing out signals that he hoped to stay on, and a number of senators of both parties are said to have joined in supporting.

His reappointment was regarded here as an important signal of the the way the new administration will approach relations with this Asian ally and eased some of the fears that a Reagan administration would be tougher in such divisive areas as defense and international trade.

A possible source of friction in the first days of the new administration will be the Japanese defense budget, the final version of which did not increase as much as the Carter administration had hoped. Until last month it had been assumed that Suzuki would press for an increase -- corrected for inflation -- of 9.7 percent, which Defense Secretary Harold Brown had reagrded as a bare minimum.

But the final version limited the increase to 7.6 percent. The restraint was largley a politcal decision, with the Ministry of Finance successfully contending that Japan could not spend more in a period when it is trying to cut back on deficit financing.

In this and in past arguments over how much Japan shoud contribute to defense in East Asia, Mansfield has counseled against pressuring Japan to reach a fixed percentage increase each year and argued that the quality and long-term intent of defense budgets were more important.