Puerto Rican terrorists yesterday claimed responsibility for bombings in Chicago and Puerto Rico, and New York police were trying to determine if they also planted phoney bombs found at Democratic and Republican party offices in Manhattan.

Terrorist groups demanding independence for Puerto Rico said the bombings were ordered -- at least in part -- as a protest against the island's inclusion in the 1980 U.S. presidential preference primaries. No injuries were reported.

A communique left on a San Juan street corner said the blasts were the results of "more than one-dozen explosive charges placed Wednesday night in Puerto Rico and the United States."

In Chicago, dynamite bombs rocked the Cook County Building. Another bomb was discovered and dismantled in a nearby building housing the Cook County Republican offices.

Another bomb made of three sticks of dynamite shattered windows in an unoccupied, one-story wooden building at the Great Lakes Naval Training Center in North Chicago. Only minor damage was reported.

Police also reported telephone bomb threats against the residence of Chicago Mayor Jane Byrne.

Three bombs shook Puerto Rico Wednesday night -- one damaging the door of a federal customs house and the others exploding harmlessly in Guanica on the island's south coast.

Also yesterday the FBI was looking into a Puerto Rican nationalist threat to blow up the Indian Point nuclear power station near Peekskill, N.Y.