Soviet claims against the United States for construction delays on its Washington embassy exceed the $29 million the United States wants for its unfinished embassy in Moscow, an official said Monday.

"We also have bills to present to the American side," Soviet Foreign Ministry spokesman Gennady I. Gerasimov told a news conference. Claims for late delivery of equipment and construction materials and other problems would top the sum U.S. officials are seeking from the Soviet Union, he said.President Reagan said Thursday that he was recommending the main office building of the new U.S. Embassy compound in Moscow be torn down because it is riddled with Soviet bugging devices.

The United States is not allowing the Soviet Union to occupy its new building in Washington until the Americans are satisfied with the status of their Moscow building.