Prime Minister Menachem Begin today turned down a request by Secretary of State Cyrus Vance to reconsider the explusion order against the mayor of the West Bank city of Nablus.

Begin said the Israeli supreme court would decide the fate of Mayor Bassam Shaka. Israeli Defense Minister Ezer Weizman defended the cabinet's decision to expel Shaka on the grounds that he was a danger to public security.

In Tel Aviv, some progress was reported in negotiations on Palestinian antonomy.

Meanwhile, in south Lebanon, Israeli and Christian militia gunners shelled Palestinian strongholds and Lebanese army positions in the south for the second day in a row, Lebanese sources said. No casualties were reported. t

A militia spokesman said a Christian militia commando unit blew up the house of a Palestine Liberation Organization supporter during a raid into PLO-held territory in south Lebanon. He said a PLO supporter was killed.

On the Israeli-occupied West Bank, aa group of Arab mayors meeting in Nablus called on Shaka to end his five-day-old hunger strike because of reports he is getting too weak.

All of the mayors in the occupied territories turned in their resignations in protest against Shaka's arrest and threatened expulsion.

Begin reportedly told Vance that Israel's decision to expel the mayor was based not only on Shaks's alleged remarks in support of Palestinian terrorism but also on his support for the PLO on the West Bank. The Israeli supreme court was scheduled to begin a hearing Thursday on an appeal of the Shaka explusion filed by his wife, Inaya.

U.S., Israeli and Egyptian teams ended the latest round of Palestinian autonomy talks in Tel Aviv and reported progress in some areas concerning the organization, conduct and Bank and Gaza Strip for a self-ruling supervision of elections in the West Palestinian council.

A senior Israeli official said the team hoped to agree on the election details when they meet again in Dec.