The London spokesman for the Palestine Liberation Organization was fatally shot in his office here today and Scotland Yard said it was looking for a young Arab suspect.

Witnesses said they saw four Arabs run from the scene of the killing in the basement of the Arab League headquarters, but police said only one man actually entered the office of Said Hamami, 34.

Hamami, a close friend of PLO leader Yasser Arafat, had been publicly disowned previously by PLO representatives in the Middle East because he advocated some form of coexistence with Israel. His public statements in Britain often took on a moderate tone.

A statement issued by the PLO esecutive committee in Beirut and the central committee of Arafat's Al Fatah guerrilla organization said, however, that Hamami was "a martyr of the Palestinian revolution" and promised to "punish the assassins."

"Killers hired by enemies of the Palestinian people, agents of Zionism and imperialiosm Wednesday shot dead the Palestinian nationalist fighter, Said Hamami, nationalist fighter, Said Hamami, reperesentive of the PLO and Al Fatah in London," the statement said.

Special Branch detectives and agents from Scotland Yard's anti-terrorist squad were dispatched to London's Heathrow Airport to prevent Hamami's assassin from fleeing the country and a massive dragnet was launched in the city.

One witness described the four men who fled the scene as young Arabs in theeir 20s. He said three jumped into a taxi and the fourth lost himself in the crowd of shoppers.

Scotland Yard said the man it was seeking was 24 years old and of Middle Eastern origin.

Hamamil's killing was the second fatal attack within a week involving Arabs in London. Scotland Yard has tentatively conculded that there is no direct connection between the PLO spokesman's murder and the car bomb that killed the Syrian medical attache and his driver on New Year's Eve, Washington Post correspondent Bernard D. Nossiter reported.

Police now think that the two Syrians may have been blown up by their own bomb, although the Syrian embassy has denied that the diplomat and his driver were carrying an explosive device.

There have been other, yet unexplained assassinations of Middle East figures in the past several weeks:

Two Arab officials in the Israeli-occupied West Bank of Jordan who were known for their cooporation with Israeli authorities were assassinated within the last two weeks. The PLO claimed responsibility from Beirut for the first murder, another Beirut-based Palestinian organization took credit for the second.

David Holden, chief foreign correspondent for the London Sunday Tiems, was killed near Cairo last month. Holden was known for his West Bank contacts. Egyptian police reports within the past week have linked the slaying to "intelligence" operations.

Plo spokesman Hamami told friends and reporters on more than one occasion that he believed extremists might assassinate him because of his moderate views.