A British tourist was shot and killed in Arab East Jerusalem yesterday, the third Briton slain in the Middle East since the U.S. air raid against Libya two weeks ago, in which Britain cooperated.

Israeli authorities said, however, that it was unclear whether the slaying of Paul Appleby, 28, of Bristol, was related to the raid on Libya, and Prime Minister Shimon Peres said there was no reason to suspect he had been singled out because he was British. Appleby was killed by a shot to his head outside the gates of the Garden Tomb, revered by many Protestants as the burial site of Christ.

In Mexico City, a previously unknown guerrilla group asserted responsibility for placing a powerful car bomb next to the U.S. Embassy Saturday and said it was in reprisal for the U.S. raid on Libya. Police defused it before it exploded.

As tensions persisted between Libya and several western countries, French police said they were placing the crew of a Libyan ship docked for repairs at Marseille under close surveillance, United Press International reported.

Turkey announced the arrest of two Libyans accused of attempting to blow up an American officers' club in Ankara on April 18, three days after the United States bombed targets in Tripoli and Benghazi after a terrorist bomb attack on Americans in West Berlin.

West German Chancellor Helmut Kohl said yesterday that he hoped leaders attending the seven-nation economic summit meeting in Tokyo next month would reach a joint agreement to combat terrorism, Reuter reported from Bonn, and the Sunday Times of London said British Prime Minister Margaret Thatcher would press at the summit for creation of a "blacklist" of suspected Libyan terrorists.

David Hirst of the Manchester Guardian reported from Tripoli that the Libyan government is expected to retaliate against the latest European Community measures to reduce Libya's diplomatic staffs in Europe.

European diplomats in Tripoli predicted that the Libyan move would take the form of a reduction in the size of the Europeans' embassy staffs there, Hirst reported. But because no European country, apart from Italy, has more than a handful of diplomats in Tripoli, the effect was expected to be small and the reductions intended as a symbolic gesture.

Some of Libya's officials were reported to be weary of the continuing confrontation, and there were indications that Col. Muammar Qaddafi wanted some breathing space -- possibly until after an Arab summit meeting expected later this week.

Jerusalem police said Appleby, who had been in Israel for about a month, may have been mistaken for an Israeli. He was bearded and wore sandals, they said, and wore nothing suggesting he was a tourist. He was found bleeding from the head by the Rev. William White, supervisor of the Protestant shrine, which is outside the walls of the Old City and about a mile from the Church of the Holy Sepulchre, which Catholics and many other Christians recognize as Christ's burial site.

The slaying took place despite increased security measures designed to protect Israelis celebrating Passover and to convince foreign tourists that Israel is safe to visit.

Jerusalem police superintendent Haim Albaldes said that he was investigating all possibilities, but that the murder appeared to be the work of Arab terrorists.

Appleby's death followed those of two British professors kidnaped in west Beirut and killed, along with an American captive, Peter Kilburn, following the air strike against Libya.

In the past two months, an American man and a West German woman, both tourists, were wounded by assailants within the walls of the Old City.

In Mexico City, a previously unknown group called the Simon Bolivar International Front said in telephone calls to local newspapers that it had planted the bomb, containing 33 pounds of gelignite, outside the U.S. Embassy, Reuter reported.

The attempt raised fears of terrorist action as the May 3 start of the Mexican World Cup soccer finals approaches. Three teams from Britain are taking part in the games, which will be held through June in seven Mexican cities.

Kohl, in a West German television interview recorded before he left Saturday for a visit to India, discussed his intention to bring the terrorism issue before the Tokyo summit meeting, which President Reagan will attend.

Kohl said he hoped the leaders would agree to closer links between their intelligence services to combat international terrorism. "A more intensive exchange of information would be a sort of early warning system, for individual countries often have advance knowledge of planned attacks or targets," he said, according to Reuter.