Moscow — The Kremlin, in its sharpest policy statement yet on the crisis in Lebanon, has in effect cautioned President Reagan not to dispatch American troops there.
Yet the Soviets still appear leery of encouraging escalation of the conflict into a full-scale showdown between Israel and the Kremlin-armed Syrians.
A senior Soviet official told an Arab diplomat privately that a military airlift to Damascus had completely compensated the Syrians for their losses at the hands of the Israelis, implying that no further arms cargoes were contemplated in the near future.
A Western diplomat interviewed July 8 said the Soviet airlift indeed had all but stopped four or five days ago. ''It seems for now,'' the envoy said, ''as if the idea was to resupply, which the Soviets did.''
The Soviets' toughened public stand, meanwhile, was evidently prompted by President Reagan's consideration of a possible dispatch of US troops to Beirut as part of a negotiated disengagement of Israeli and Palestine Liberation Organization forces.
Reflecting the depth of Soviet concern that the Americans could yet emerge from the Lebanon crisis with reinforced Mideast influence - and military presence - the Kremlin responded with great speed.
The reply came in the form of a letter over President Leonid Brezhnev's signature. The note is understood to have been sent ''about a couple of days ago.'' Its receipt did not visibly prod a move to abandon consideration of the possibility of sending the US troops, and on July 8, the official Soviet news agency, Tass, chose to make parts of the letter public.
While quoting Mr. Brezhnev as expressing hope that the US role in the crisis would not be determined by ''opportunistic calculations,'' Tass said:
''In connection with statements to the effect that the USA, in principle, is prepared to send a contingent of American troops to Lebanon, Leonid Brezhnev warned the United States President that if this really took place, the Soviet Union would build its policy with due consideration of this fact.''
What precisely this would mean, Tass's release on the Brezhnev note did not say. The letter appeared to have stopped short of the explicitly ominous tone adopted by the Soviets near the end of the 1973 Mideast war.
Then, the Soviets themselves had feinted at sending troops to the region as part of a joint superpower peace-keeping force, something Washington was set on preventing. A Brezhnev note at the time said the superpowers should dispatch troops ''without delay,'' and added: ''I will say it straight, that if you find it impossible to act jointly with us in this matter, we should be faced with the necessity urgently to consider the question of taking appropriate steps unilaterally . . . .''
Still, the July 8 Brezhnev note seemed at variance with what departing US Secretary of State Alexander M. Haig Jr., in mid-June, called the ''encouragingly cautious'' approach of two earlier Brezhnev communications on the Lebanon crisis.
Although the US Embassy would not comment on details of superpower communications on the crisis, other Western diplomats here said July 8 they understood there had been at least one other Brezhnev note in addition to those publicly mentioned. But the diplomats did not characterize the contents.
Diplomats here suggest the Kremlin's next move will depend largely on US action, and on developments on the ground in Lebanon.
But the latest Brezhnev letter, they say, contains no indication the Kremlin is yet in the mood to risk a superpower confrontation, or a widened Mideast war, over the crisis in Lebanon.
Ranking Soviet officials were not immediately available for comment on the note from Brezhnev.