Secretary of State Alexander M. Haig Jr., seeking to ease Greece's concern about the security of its eastern border with Turkey, today cited U.S. policy on the Falkland Islands crisis as proof that the United States opposes settlement of territorial disputes by force.

Haig, who spoke at a press conference before leaving for a NATO foreign ministers' meeting in Luxembourg, was questioned repeatedly about how the Reagan administration will respond to Greek demands for some kind of U.S. guarantee for the sovereignty of Greece's borders in the Aegean Sea area.

Prime Minister Andreas Papandreou's government has said that such a guarantee is required if Greece is to renegotiate a continuation of the 1953 agreement under which the United States operates four important military bases in this country.

"The U.S. view is no different than it is in the Falklands question," Haig said. "We reject and oppose the first use of force to resolve disputes. This is a matter of principle."

Haig, who repeatedly stressed the "cordial and constructive nature" of his talks with Papandreou, also implied that the two sides were moving closer to a resolution of the thorny bases issue.

Papandreou, who was elected last October in a campaign with strong anti-American overtones, said at the time that he wanted to negotiate the closing of the U.S. bases. He since has adopted a more moderate stance, but Greek sources stress that domestic political considerations require him to move cautiously on the issue.