Prime Minister Menachem Begin today accepted the resignation of Avraham Achituv, the head of the Israeli security services who was the focus of a political controversy surrounding the investigation of assassination attempts against three West Bank mayors in June.

A new security services head was named to replace Achituv, but his name will remain a secret in keeping with government policy, an Israeli Cabinet official said.

Achituv's name was disclosed when The Washington Star reported that he had decided to resign as a protest because Begin had attempted to obstruct the investigation of the car bombings of three Palestinian mayors. The government denied the report and said Achituv had announced his plans to retire before the assassination attempts.

Nablus Mayor Bassam Shaka lost both legs and Ramallah Mayor Karim Khalaf lost a foot in the bombings, which ultranationalist Jewish settlers are thought to have carried out. No arrests have been made in the cases.

Begin vigorously denied The Star's report that Achituv, head of General Security Services (Shin Bet) had requested a special task force to infiltrate the ultranationalist Gush Emunim settlers' organization and that Begin insisted that the case be handled routinely by the police and other investigative agencies.

In an extraordinary public statement, the security chief went on Israeli radio condemned the report as a "total fabrication." The government initiated criminal action against the reporter, David Halevy, for violating the state secrets act by disclosing Achituv's name. But Halevy, an Israeli citizen, has remained out of the country.