Secretary of State Alexander M. Haig Jr., following lengthy talks with Soviet Foreign Minister Andrei A. Gromyko, today left open the possibility of new negotiations to reduce strategic armaments despite a "long, dark shadow" cast by Poland on all aspects of Soviet-American relations.

In a somber report on the nearly eight hours of talks--about twice as long as had been planned--Haig said he told Gromyko that the United States is "actively engaged" in preparations for strategic arms negotiations to be initiated "when conditions permit."

In a Tass report from Moscow that appeared soon after the end of the talks, the Soviet Union characterized the Haig-Gromyko session as "necessary and useful."

Before martial law was declared in Poland last month, Haig had U.S. AWACS planes detected two Soviet bombers that penetrated U.S. airspace.Page A17 planned to use today's meeting to set a date for the beginning of the Reagan administration's strategic arms reduction talks, which it refers to as START.

In a gesture of disapproval of Soviet involvement in the Polish crackdown, no date was set today. Speaking at a press conference following the meeting, Haig repeatedly declined to define the necessary conditions for the beginning of START. He specifically refused to rule out participating in talks before martial law is lifted in Poland.

Like the first round of Haig-Gromyko talks in New York last September, today's discussions were described by Haig as ranging over a full panoply of U.S. concern about Soviet activity in Afghanistan, Central America and Southern Africa. Haig said an "extensive" and "very detailed" part of the talk was about Soviet backing for Cuban activity in Africa and Central America, including U.S. intelligence reports of new model MiG warplanes being shipped to Cuba in recent weeks.

But his primary focus, Haig told reporters, was the situation in Poland, which "cast a long and dark shadow over all of the discussions regarding East-West relations."

Gromyko declared on arrival here yesterday that he did not intend to discuss events in Poland and the Tass report tonight said "attempts of the U.S. side to make problems pertaining to events in the Polish People's Republic were rejected...as incompatible with the principle of non-interference in the internal affairs of sovereign states." Haig put a different interpretation on the subject, however, saying that there was "a two-sided discussion" of the Polish problem "within the context of the clear attitude of the Soviet Union that this is an internal affair."

Gromyko did not appear with the U.S. secretary of state at the close of their meetings, as was customary in the 1970s when Soviet-American relations were better.

There was relatively little of the banter which characterized earlier appearances of Gromyko and his American counterpart in brief photo sessions for journalists. Both men appeared unusually serious. Haig seemed to be tired and drawn after the long meetings.

Haig said there was no discussion today of a summit session of President Reagan and Soviet President Leonid Brezhnev. Nor, he said, was there an agreement about a next round of talks with Gromyko.

At the same time, Haig expressed satisfaction at today's "very sober...extremely detailed" exchange, which he described as a "necessary communication" at the right time in a period of Soviet-American tension.

Haig appeared to be seeking to avoid the appearance of "business as usual" with the Russians, which is offensive to much American opinion under current circumstances. But he seemed also to be trying not to give the appearance of U.S. intransigence about Soviet-American communications and arms control efforts, which are politically important as well, especially so in Western Europe.

The session with Gromyko was reduced by Haig to one day rather than two in a gesture related to Poland. But as it turned out, the 7 3/4 hours spent in the morning and afternoon sessions today were not much short of the 9 1/2 hours over two days last September.

All of today's talks, like the great majority last September, were head-to-head discussions between Haig and Gromyko, accompanied only by their interpreters.

Asked whether progress had been made, Haig replied this was not the purpose of the U.S. side, which saw it primarily as an opportunity to express clearly its concern about the situation in Poland.

Possible future sanctions, which have been threatened by Reagan if the situation in Poland remains unchanged, were discussed, according to Haig, but he refused to elaborate.

While saying that Soviet-American differences in some areas remain wide, he added that there are "obvious prospects" for progress in others. He expressed hope that progress will be made in the continuing negotiations over the limitation of medium-range nuclear missiles in Europe. While saying he had explained U.S. proposals in detail, however, Haig reported no sign of Soviet movement.

The discussion of some topics "carried forward in constructive ways" the dialogue of last September, but other areas remained "on the rocks of disagreement," said Haig. He did not elaborate.

Haig said that in addition to international affairs he took up with Gromyko bilateral humanitarian issues such as the emigration of Soviet Jews, the plight of Pentecostal Christians camped in the U.S. Embassy in Moscow and individual human rights cases.

Haig is scheduled to leave early Wednesday for brief visits to Israel and Egypt before returning to Washington late Friday.

Gromyko is reported to be planning to leave early Wednesday for East Germany before returning to the Soviet Union.