The search for Michael Dukakis' running mate began in earnest Tuesday as his manager traveled to Washington to discuss prospects, and rival George Bush courted the Cuban-American vote with some sharp words for Fidel Castro.

Dukakis was in Washington to address a NATO group, plugging his alternative to President Reagan's "Star Wars" and his plans for strengthening the European alliance.Dukakis campaign chairman Paul Brountas, point man in the Democrat's search for a running mate, was to spend several days in Washington to discuss vice presidential prospects.

Campaign aides said Brountas would seek advice from members of Congress and other Democratic Party leaders.

Dukakis gave the Atlantic Council, a private, pro-NATO group, his assessment of the recent U.S.-Soviet summit and called for negotiations between NATO and Warsaw Pact countries on conventional military forces.

"We don't need SDI; we need CDI, the Conventional Defense Initiative begun by leaders in the Congress to apply advanced technology to the challenge of fighting and winning a conventional war," the Massachusetts governor said.

Dukakis praised the U.S.-Soviet treaty banning intermediate-range nuclear missiles, and he hailed President Reagan's stance on human rights at the recent Moscow summit.

But Dukakis criticized the administration, saying the United States should never again "announce radical changes in our strategic doctrine or adopt dramatic new bargaining positions on nuclear weapons without consulting our allies."

Bush met on Monday with members of the Cuban-American National Foundation, an anti-Castro group. "There have been no accommodations made with Castro's corrupt communist government by this administration and, if I may inject a partisan point, I guarantee you there will be no accommodations" during a Bush presidency, he said.