A bomb that exploded late Tuesday night in front of the National War College Building at Fort McNair in Southwest Washington caused an estimated $100,000 in damage, a military spokesman said yesterday.

The blast shattered windows and cracked walls in the four-story building designed by noted architect Stanford White, at about 10 p.m. The device was placed in an 18-inch-high concrete vase that was at the entrance of the War College building, the spokesman said. No one was injured in the blast.

Fifteen minutes before the explosion, calls were made to the Pentagon switchboard and United Press International warning that a bomb was about to go off. The caller, who had apparently tape recorded his message, made a vague reference to U.S. bases in Guatemala. He also mentioned "U.S. imperialism," according to UPI.

A spokesman for the FBI said yesterday that there is no reason to think Tuesday's explosion has any connection with a firebomb that damaged an office in the environmental crimes division of the Justice Department on Pennsylvania Avenue, NW, at about 8 p.m. last Saturday. No one has claimed responsibility for that incident.

The National War College trains about 175 senior military officers a year in advanced war strategy. The base is situated on Greenleaf Point at the convergence of the Anacostia River and the Washington Channel.

Security personnel yesterday were taking down the license tag numbers of cars entering the base without military parking stickers. No other security precautions were in effect, and classes were being conducted as usual.

The FBI said it is examining fragments from the bomb but has not concluded the nature of the device or how it was detonated.