Secretary of State Alexander M. Haig Jr. arrived here today on the first leg of a trip to assure Turkey and its neighboring antagonist, Greece, that the United States considers both vital to the North Atlantic Treaty Organization's southeastern flank.

Haig's visits here and in Athens, to be followed by his attendance at the NATO foreign ministers' meeting in Luxembourg next week, marks his return to normal diplomatic activity after more than a month of almost exclusive concentration on the Falkland Islands crisis.

In the Reagan administration, U.S. relations with Turkey have been warmer than with Greece. The United States, in marked contrast to several Western European members of NATO, has praised the "law and order" achievements of the martial-law rule established under Gen. Kenan Evren after a 1980 military coup.

U.S. officials with Haig said that policy would continue despite the criticism directed against Evren's government in Western Europe for its arrest of former prime minister Bulent Ecevit and many other domestic dissidents.

In the U.S. view, they said, Turkish authorities are more likely to respond to persuasion than to pressure. In addition, they said, the administration feels that the military government has made dramatic progress toward eliminating terrorism and in restoring a measure of health to Turkey's economy.

Turkish expectations that U.S. support will continue were underscored by Foreign Minister Ilter Turkmen when he greeted Haig. Turkmen noted that his government's timetable calls for restoring democratic processes by the fall of 1983 and added: "We feel that in this undertaking we deserve the confidence and unswerving support of our allies."

Haig was noncommittal in his response. But U.S. sources said privately that the administration plans to ask Congress to boost military and economic aid to Turkey to more than $800 million in 1983. Much of this assistance is for modernizing Turkish military equipment, including replacement of its aging aircraft with a combination of new, U.S.-made F16s and F5Gs.

In addition, while U.S. officials stressed that Haig does not contemplate any mediating role, he is expected to explore the chances for easing Greek-Turkish tensions over Cyprus and disputed borders in the Aegean Sea.