The top executive of a West German engineering company that produces engines for NATO tanks and aircraft was shot and killed by a gunman apparently acting for the Red Army Faction, which claimed responsibility for the attack.

The killing of Ernst Zimmermann, 55, was the first assassination by the left-wing terrorist group of a public figure in West Germany since a wave of bomb and arson attacks was launched, primarily against military installations, two months ago.

The shooting today coincided with eight bombings in Portugal that damaged cars and homes of servicemen from a West German air base. The explosions were claimed by the same Portuguese underground guerrilla group, FP-25, that said it was responsible for a mortar attack against NATO warships in Lisbon early this week.

The killing of Zimmermann was the second in a week of a European who figured prominently in his country's arms industry. The French terrorist group Direct Action shot and killed Rene Audran, a senior French Defense Ministry official in charge of arms exports, near his home in Paris Friday night a week ago. The Red Army Faction recently announced that it was joining forces with Direct Action.

The federal prosecutor's office in Karlsruhe said Zimmermann was shot once in the head by a young man with a submachine gun who forced his way into the industrialist's suburban home after his wife opened the door to a woman purporting to carry a hand-delivered letter.

The pair of attackers, believed to be in their 20s, bound up the couple, gagged the wife and dragged Zimmermann to a bedroom where he was shot. He later died in the hospital of his wounds.

The killing raised fears that the Red Army Faction is prepared to escalate its campaign from attacks on property to the kind of murders and kidnapings that marked West Germany's last spasm of terrorism in the 1970s.

The recent surge of violence began when 30 convicted Red Army Faction terrorists scattered in various jails embarked on hunger strikes Dec. 4 to dramatize demands to be grouped together as political prisoners. Some have abandoned their fast but others are now very weak, and police have feared possible assassination attempts against leading politicians and businessmen if any of the hunger strikers should die.

Zimmermann was the chief executive of MTU, or Motoren und Turbinen Union. The company builds engines for the Leopard II battle tank and the Tornado advanced fighter plane.

Police said details about Zimmermann were found in notes confiscated when a terrorist hide-out was raided last year. Information seized during the raid reportedly led to the arrests of several leading members of the Red Army Faction.

Federal investigators said they also were examining a letter sent to the tabloid Bild that threatened the lives of 10 prominent West Germans, including Chancellor Helmut Kohl and his predecessor Helmut Schmidt. Zimmermann's name was not on the list, however.

The letter reportedly warned that the terrorists would kill one person on the death list for every hunger striker who dies. It was signed by the Commando Holger Meins, a name referring to one of the first leaders of the Red Army Faction, then known as the Baader-Meinhof gang, who starved himself to death in prison in 1974.

Four hours after the shooting, a Munich newspaper received a telephone call from someone alleging that the Commando Patrick O'Hara had carried out the attack. Bavarian police said Patrick O'Hara was an Irish Republican Army terrorist who died in Belfast May 22, 1981, following a hunger strike.

Federal police said the caller, whose claim was being treated as authentic, also said, "the West European guerrilla movement is shaking the imperialist system." The officials said the call reinforced their belief that the Red Army Faction was seeking to expand contacts and cooperation with other terrorist groups in Western Europe.

Since the hunger strikes began, more than 60 bombings and arson attacks have taken place in West Germany, inflicting $8 million worth of damage, according to West German officials.

Interior Minister Friedrich Zimmermann said the "new flare-up of terrorism" has occurred even though only between 20 and 40 members of the Red Army Faction are believed to be actively engaged in violent activities. They, in turn, are supported by up to 150 sympathizers who provide lodging and passive assistance, he said.

On Jan. 15, the Red Army Faction said it was joining forces with the French leftist underground group Direct Action to form a "political-military front in Western Europe" to launch strikes against NATO installations.

A Belgian group, the Fighting Communist Cells, is also believed to working closely with French and German left-wing terrorists. West German antiterror specialists said it has been determined that all three groups have used the same explosives stolen from a quarry near Ecaussines, south of Brussels, last June.

The Belgian group has claimed responsibility for 13 attacks on military targets since October, including 6 bombings at a NATO fuel pipeline.

Special correspondent Peter Wise reported the following from Beja, Portugal:

Eight bomb blasts destroyed servicemen's automobiles and damaged homes near a West German Air Force base in this southern Portuguese town early today.

The Popular Forces of April 25 told news agencies it had planted the bombs to demand the dismantling of military installations and the explusion of foreign servicemen. It was the group's fifth strike against NATO or American targets in Portugal within three months.

West German Embassy spokesman Juergen Kreighoff said the bombs began exploding at intervals of between one and 11 minutes shortly before 2 a.m. local time, totally destroying eight cars, seriously damaging 10 others, and blowing in doors and windows in the tree-lined suburb where more than 800 German military personnel and their families live.

Kreighoff said the wife of a serviceman was cut by flying glass after she went to a window following the first blast, but there were no other injuries. The bombs were all placed under automobiles with distinctive license plates showing they belonged to foreign servicemen, according to police. West German antiterrorist officials were due here late today to pursue investigations.

The West German community where the bombs exploded is on the outskirts of this wheat-farming town, 140 miles south of Lisbon, and five miles from the base built by West Germany in 1962 as a training center for military pilots.