France's new right-wing prime minister, Jacques Chirac, promised today to step up antiterrorist cooperation with other western countries following a series of bomb attacks here that have left two persons dead and more than 80 injured.

The prime minister's pledge, made on his second day in office, came after a meeting with Secretary of State George P. Shultz in which terrorism was discussed. In the past, U.S. officials have criticized privately what they see as France's reluctance to cooperate fully against terrorism.

In Beirut, meanwhile, an extremist group calling itself the Committee for the Release of Arab Prisoners asserted responsibility for the latest bomb attack in Paris last night, moments after the transfer of power to Chirac by the outgoing Socialist administration. The group threatened further attacks in the streets of Paris and Rome unless the French and Italian governments freed convicted or suspected terrorists.

Terrorism is a particularly sensitive subject for the new right-wing government because it made respect for law and order an important issue in the recent election campaign. Chirac, 53, already has promised to take a series of measures to strengthen security, including the reinstitution of random identity checks in the streets, a practice abolished by the previous Socialist government.

"I told the secretary of state that my government wanted a significant strengthening of coordination between our democracies so as to struggle more efficiently against terrorism," Chirac told reporters after his meeting with Shultz.

French police issued a description today of a young man, of "Middle Eastern" appearance, suspected of leaving a powerful nail bomb on a commuter train last night shortly after a bomb exploded on the Champs Elysees. The second bomb, which could have caused many deaths had it exploded, was defused by police after an alert passenger noticed an unattended bag.

The latest bombings appeared to mark the escalation of a campaign against France that began last December with attacks on two large department stores in central Paris. Last night's bomb, which killed two persons and injured 28, was the most powerful explosion to date. Nine of the injured are still in serious condition after overnight operations.

In its latest statement, the Committee for the Release of Arab Prisoners denied that it was linked with pro-Islamic groups in Beirut that have seized eight Frenchmen during the past year. French investigators noted, however, that all the groups that have asserted responsibility for terrorist acts against France have made similar demands.

Today's Beirut statement demanded the release of three men held in France: Georges Ibrahim Abdallah, also known as Abdel- Kader Saadi, arrested in Lyons in 1984 for carrying false identity papers and suspected of being a leader of the Lebanese Armed Revolutionary Faction; Waroujan Garbidjian, an Armenian nationalist sentenced to life imprisonment for a 1983 Orly Airport bombing that killed eight persons, and Anis Naccache, serving a life sentence for trying to kill former Iranian prime minister Shahpour Bakhtiar in 1980.

Chirac said he was "horrified by the beastly and inhumane character" of the bombings. Promising a "very significant strengthening" of measures to fight terrorism, he said "much more systematic" searches would be carried out in public places considered at risk.

Chirac did not specify the measures planned to strengthen international cooperation against terrorism. In the past, French governments have authorized the exchange of information between police forces but have resisted U.S. attempts to press the terrorist issue at annual western summits.

In addition to calling for the release of terrorists from French jails, the Beirut kidnapers also are reported to have demanded the withdrawal of French military observers from Lebanon and an end to French support for Iraq in its war with Iran.

Special correspondent Nora Boustany added from Beirut:

The Committee for the Release of Arab Prisoners also demanded that Italy release Josephine Abdo Sarkis, suspected of a 1984 attack on a United Arab Emirates diplomat in Rome, and Abdullah Mansouri, caught with a suitcase of explosives on an Italian train.