A bomb caused extensive damage today to the European headquarters of the U.S. defense contractor Honeywell, just several hundred yards from the entrance to NATO headquarters.

The bombing was the third against a business office in Brussels in a week and was claimed by the Communist Combatant Cells, the same shadowy group that took responsibility for the other two attacks.

In a letter delivered to a Brussels television station, the group said it had targeted Honeywell because of its links to the North Atlantic Treaty Organization's medium-range nuclear missile program -- the same motive it gave for the previous attacks.

The bombing was part of "the anti-imperialist campaign of October," the letter said, saying that Honeywell is "actively involved in the construction program of cruise missiles" -- which, with Pershing II missiles, are being deployed in Western Europe for the first time by NATO.

The suitcase bomb apparently was left against a door of the Honeywell complex, where 140 persons work, in the Brussels suburb of Evere, about a quarter of a mile down a four-lane highway from the NATO headquarters.

Terry Lawrence, a Honeywell spokesman in Brussels, said the 5 a.m. explosion caused no injuries but damaged 15 rooms on two floors, as well as hallways and stairways.

Four guards were on duty at the time of the blast, he said, two of them patrolling with dogs and the other two at fixed posts in the complex. They said they saw nothing before the explosion.

Lawrence said American divisions of Honeywell make radar alternators for cruise missiles to control their altitude during flight, and the company is a subcontractor for in-flight stabilization mechanisms for the Pershing.

He said that while Honeywell's Brussels office handles aerospace and defense business, it is also the European headquarters for the company's affiliates "mainly working in the fields of control products and control systems." These products include air conditioning and heating units, electronic components and petrochemical control systems.

A NATO spokesman would not comment on the attack. No extra guards were observed this evening at the main entrance gate to the NATO headquarters.

Belgian officials say they know little about the Communist Combatant Cells, including whether the group has links to Direct Action, the French leftist group that has claimed responsibility for several recent bombings in Paris.

Belgium has been spared most of the home-grown terrorism that has troubled many European countries in recent years, but it has often served as a battleground for foreign groups. The West German Red Army Faction claimed responsibility for the 1979 bomb attack against Alexander M. Haig Jr., then commander of NATO.

One of the attacks last week, against the division of the American Litton Co., took place about a half-mile from NATO headquarters. The other was against the offices of a West German truck manufacturer on the other side of the city. Neither attack caused any injuries.