Arab terrorists attacked an El Al airline crew in broad daylight yesterday, hurling grenades and firing bursts from automatic weapons in the heart of this capital.

When the brief carnage was over, an Israeli stewardess and one of the gunmen were dead and nine other persons injured. The gunman was a victim of recocheting fragments from his own grenade.

Another attacker was chased and caught by police in a squad car. A third attacker escaped.

Last night, a Palestinian extremist group acknowledged reponsibility for the assault. The Popular Front for the Liberation of Palestine - Special Operations telephoned Reuter news agency here to say the attack was a "last warning against use of the Israeli airline El Al."

This is the group that hijacked a West German airliner to Somaha last October. The plane was recovered by German commandos.

Diplomats said they thought the attack was connected with the forthcoming meeting at Camp David, where President Carter President Anwar Sadat of Egypt and Prime Minister Menachem Begin of Israel will seek to revive negotiations for Middle East peace. The assault, it is thought here, was intended as a grim insistence that no peace is possible without Palestinian assent.

The assault took place just off fashionable Grosvenor Square, a few hundred yards east of the U.S. Embassy. Dozens of stunned bystanders, passing in front of the Europe Hotel where the crew was attacked, dove for the pavement and watched the affair in horror . So did patrons at a nearby pub, many of them taking a Sunday beer in the warm sunshine outside.

Of the nine persons hit by bullets, grenade sprinters and flying glass three were reported to be in critical condition.

One of those seriously injured is also an El A1 air hostess. Another hostess is among the less critically hurt. All the other injured were passers-by.

It was the first against any Israeli institution here since an agricultural attache at the Israeli embassy was killed by a letter bomb in 1972.

More recently, inter-Arab feuding has resulted in several assassinations and near assassinations in London.

The El Al crew had just flown here from New York and unloading its bus at the Europa entrance on Duke Street. Suddenly, the gunmen apeared, firing two submachine guns and hurling three grenades. A stewardess, whom witnesses said had half her head blown off, was killed at once.

Then, according to Alan Fykin, the Europa chef, two men "rushed into the kitchen and tried to get hold of some chefs' uniforms."

But they abandoned this peculiar strategy and dashed out again. Dozens of police came to the scene within minutes and a squad car spotted a running man. Another witness, John Harris, saw the chase.

"A police car screamed down the wrong way of a one-way street after an Arab who was running away," he said. "Three men jumped out of the car and pounced on the Arab, who was shouting, screaming and kicking. They managed to handcuff him and take him away."

Scotland Yard has poured in resources, technical and physical, to hunt for the third man. Forensic experts carefully picked up debris in Duke Street, which was cordoned off with white tape. Commander Jim Nevill, chief of the yard's anti-terrorist branch, deployed a battery of detectives to question the many witnesses. Police came with dogs to sniff out the runaway's trail.

In the call to Reuter, the Palestinian group's spokesman asserted that "El Al is a military institution used to carry spare parts and volunteers to Israel for use against the Palestinian people." Therefore, El Al is "a military target" and the group "will strike at it wherever it can."