A bomb exploded in the Rome office of British Airways today, injuring 14 people, four of them seriously. A 16-year-old Palestinian identified as Hasan Aatab was arrested running away from the scene and later admitted having tossed the bomb into the airline office, police said.

It was the second bomb in 10 days in the Via Veneto area, which in this season is crowded with tourists and shoppers.

Aatab, who was born in the Shatila refugee camp near Beirut and was carrying a Moroccan passport, told investigators he belonged to the Revolutionary Organization of Socialist Moslems, authorities said.

That group, which charges that Rome is a center for U.S. and British spying on behalf of Israel, also claimed responsibility for the bombing of a Via Veneto cafe on Sept. 16 that injured 39 people, mostly tourists. A Palestinian also was arrested running away from that bombing, but has not confessed to taking part in it, according to police sources.

The bomb today destroyed the airline's ticket office in Via Bissolati, around the corner from the U.S. Embassy. The office's plate glass windows were shattered and passers-by were covered with rubble and shards. Most seriously injured were three British Airways employes and a passer-by.