BERLIN (AP) _ West German President Richard von Weizsaecker met Monday with eight U.S. soldiers wounded in last month's nightclub bombing and later said he understood why the United States struck at Libya.

After visiting the U.S. Army's Andrews Barracks in West Berlin, Weizsaecker said the eight servicemen and their families ''seem to have overcome the injustice that befell them'' at the La Belle discotheque, bombed by terrorists on April 5.

The eight servicemen have recovered from injuries suffered in the attack that killed a U.S. Army sergeant and a Turkish woman. At least 230 people were wounded, including 63 Americans, in the nightclub that was a popular meeting place for Berlin-based U.S. troopers.

President Reagan blamed terrorists who he said were backed by Libya and on April 15 U.S. warplanes bombed the Libyan cities of Tripoli and Benghazi.

''I have the fullest understanding'' for the air strikes, Weizsaecker said in a short speech to U.S. military officers after visiting the servicemen.

''And I feel it was not only inevitable but right to prove that the (West German) government - like the American government - is not prepared to sit and do nothing when they see that their citizens and their friends are put in mortal danger by those madmen.''

West Germany and the 11 other European Common Market nations, under U.S. pressure for months to crack down on Libya, imposed diplomatic sanctions against the radical Arab state in late April.

Weizsaecker told the officers that West European reluctance in joining U.S. sanctions against Libya was ''not a delaying tactic.''

''We have the same goals, but we're not sure if sanctions against Libya is the proper way to rid the world of terrorism.''

The army identified the eight injured soldiers as:

Staff Sgt. Carlos Marquez, 26, of San Juan, Puerto Rico; Pfc. Leroy Craig, 20, of Suffolk, Va.; Pvt. Timothy Henderson, 19, of Dallas; Spec. 4 William Johnson, 21, of Cordele, Ga.; Spec. 4 Larry Lampkins, 34, of Milwaukee; Spec. 4 Gerald Ford, 26, of Albany, Ga.; Spec. 4 Tracy Billingslea, 22, of Unadilla, Ga., and Spec. 4 J.C. Andrews, 22, of Atlanta.