A left-wing terrorist group known as the Revolutionary Cells claimed responsibility for three bomb attacks in two West German cities today to protest the seven-nation economic summit that opens here Thursday.

The explosions in Cologne and Duesseldorf ripped through offices of the Deutsche Bank, the country's leading bank; the giant chemical firm, Hoechst, and the metal industry's employers association, police said. Nobody was injured in the blasts, which occurred almost simultaneously early this morning.

The fear of terrorist actions during the meeting of seven top leaders of noncommunist industrialized world -- including President Reagan -- has instigated the largest security operation ever undertaken in West Germany, according to officials of Bonn's Interior Ministry.

Up to 10,000 police have been mobilized to seal off Bonn's government quarter, where the summit will take place, from demonstrators and potential assailants.

The Interior Ministry intends to make the airspace above Bonn off-limits to all private planes and has instructed police to bolt down manhole covers to prevent would-be terrorists from intruding into the summit area through the capital's sewer system.

A letter was sent to a Cologne newspaper signed by the Revolutionary Cells, a radical left-wing terrorist group known to have connections with the Red Army Faction, which has carried out killings and kidnapings of prominent West German politicians and industrialists.

The message said, "World capital will be uniting to celebrate in the spirit of conquest while social achievements are being undermined with unbelievable effrontery."

Another newspaper in Cologne also received a letter contending that the bombs were detonated in retaliation for what was described as "the plundering of the Third World" by West German banking and business concerns.

Police officials said they were convinced that the claims of responsibility were genuine. The Revolutionary Cells have carried out several acts of sabotage in recent months that have caused extensive damage but no deaths or injuries.

Heinrich Boge, the president of the Federal Criminal Office, said today that the bombings were probably a prelude to further attacks timed to coincide with the summit.

"Violent terrorists and groups sympathetic to them intend to stage further spectacular attacks in order to maximize their propaganda against the western political and economic system," Boge said.

The most likely targets, he added, were people and buildings considered to be "representative of the imperialist system."