Pope John Paul II will come to the United States in early October to address the United Nations and will meet with President Carter.

Neither the White House nor the Vatican would discuss any details of the visit, which has been rumored since the pontiff's trip to Poland in the spring, but authoritative sources have confirmed that it will take place.

An invitation to visit the United Nations was extended to the pope by Secretary General Kurt Waldheim last May. Church sources have indicated the pope want to make such a visit early in his pontificate to dramatize his strong support for the international organization.

Pope Paul VI, who died last year, also visited the United Nations, making one of his most widely remembered antiwar statements there in 1965. But apart from a quick tour through New York City and an evening service at Yankee Stadium, he made not other visits in this country.

There has been widespread speculation about other cities that Pope John Paul, who visited this country twice while he was still a Polish cardinal, might visit.

Conjectures on the most likely itinerary mention, - in addition to New York and Washington - Philadelpha, Los Angeles, San Francisco, and possibly Orchard Lake, Mich., near Detroit, the site of a seminary that trains priests with Polish ethnic background.

The National Conference of Catholic Bishops, which is exptected to coordinate plans for the papal visit here, has tentatively reserved blocs of hotel rooms in New York and Washington for several weeks in anticipation of the visit. Last week the bishops' conference added a staff member, the Rev. Robert Lynch of Miami, to handle arrangements for the visit.

Some church observers have speculated that the Vatican delay in announcing the plans may stem in part from problems of the church in the Chicago Archdiocese. Chicago Cardinal John Cody has for years been at odds with Priests of his archdiocese.