Secretary of State Alexander M. Haig Jr. said tonight that he and Prime Minister Andreas Papandreou were making progress on resolving the strains in U.S.-Greek relations including the thorny issue of maintaining American military bases in Greece.

Talking with American reporters, Haig said he and Papandreou had agreed not to discuss details of their talks until his visit ends Sunday. But he repeatedly described the discussions as "extremely cordial and constructive" and added, "My own personal assessment is that we have made progress on all key substantive topics involving U.S.-Greek relations. Thus far it has been a very productive visit."

One key issue is the future of four American military bases here, which Papandreou said during his election campaign last autumn that he wished to close.

Papandreou told reporters after the first round of talks that none of the issues discussed was solved but added, "The talks were sincere and straightforward, and I am satisfied," Reuter reported.

Haig came to Athens following a two-day visit to Turkey, and the continuing antagonisms between Turkey and Greece had been expected to cast a shadow over the Haig-Papandreou meeting. Both nations are partners of the United States in the NATO alliance, but under President Reagan, U.S. relations with the martial-law government of Gen. Kenan Evren in Ankara have been warmer than those with Athens.

Strong U.S. backing for Evren's tough crackdown on terrorism within Turkey, coupled with big increases in American military and economic aid, have fueled anti-American feeling within Greece and stirred charges of a U.S. "tilt" toward Turkey.

At his Ankara press conference, Haig continued to praise the Evren government in lavish terms and, in what appeared to be a reprimand to West European governments that have criticized the repressive tactics of the Turkish government, he recalled the terrorism and economic chaos that plagued Turkey prior to the military takeover in September 1980.

"Sometimes I think memories are too short," Haig said. He also declined to discuss the government's imprisonment of former Turkish prime minister Bulent Ecevit, which has been one of the principal causes of the West European criticism.

"It would not be appropriate to make any public comment on an internal matter that is being pursued in accordance with Turkish law," he said. "I didn't discuss it, but it was discussed with me by Turkish authorities."