The Reagan administration, hoping to stabilize the shaky cease-fire between Israel and the Palestine Liberation Organization, intends to broaden the mission of special Middle East envoy Philip C. Habib to include the security problems of southern Lebanon, a senior U.S. official said tonight.

An immediate priority, the official said, is the strengthening of the 2,000-member U.N. force in southern Lebanon (UNIFIL) and the broadening of its areas of patrol. Habib, who was at the United Nations earlier this week, already may have begun discussions along these lines.

The U.S. plans, described as part of a "more comprehensive Lebanon settlement approach," were made known by the familiar senior official who often speaks on background to reporters during travels of the secretary of state, in this case, Alexander M. Haig Jr.'s trip to a North-South foreign ministers' meeting here starting Saturday.

When Habib returned to Washington a week ago after announcing the cease-fire between Israel and the PLO in Lebanon, there were broad hints that he wished to terminate the strenuous mission that has kept him on a nearly continuous round of travel and consultation for nearly three months.

The broadening of Hgabib's mission indicates the contrary. The retired diplomat will be "in and out" of the Middle East as needed during the coming period, reporters on Haig's plane were told.

The original Habib mission -- arising from a threatened clash between Israel and Syria over the placement of Syrian antiaircraft missiles -- dealt almost entirely with northern Lebanon. After Israeli-PLO battles suddenly flared in the south this month, Habib concentrated on obtaining a quick cease-fire. But he had little involvement in the underlying tensions and conflicts of southern Lebanon.

Beyond the strengthening of UNIFIL, the United States also intends to make additional efforts to strengthen the Lebanese central government, according to the official.

Haig is hoping for additional financial and political backing for the Lebanese government from European allies as well as leading Middle East nations. This weekend's North-South event here, which involves 212 nations, will provide an opportunity to advance this cause during bilateral discussions.