Secretary of State Alexander M. Haig Jr. has dispatched a senior emissary to Iraq after receiving new signals of Baghdad's interest in repairing and perhaps restoring long-shattered U.S. relations, according to officials in the Haig party.

The emissary, Deputy Assistant Secretary of State Morris Draper, is now en route to Baghdad carrying a message of interest on the part of Washington, sources said.

A principal obstacle to improved U.S.-Iraqi relations has been the longstanding Iraqi position that the United States must change its policy of support for Israel, and there was no indication that Iraq had changed that position.

In the Reagan administration's view, it is up to Iraq to make the first move to restore relations, since it was the Baghdad government that broke them off nearly 14 years ago, at the time of the 1967 Arb-Israeli war.

Washington, however, did its part in displaying good will a few days ago by approving the sale of five new Boeing jetliners to the Iraqi national airliner, in a reversal of previous U.S. policy.

Haig, testifying March 19 before the Senate Foreign Relations Committee, was surprisingly resistant to senators' suggestions of a tough line against the often radical Iraqi government, which remains of the official U.S. list of countries supporting terrorism and recently was charged by Sen. Alan Cranston (D-Calif.) with seeking a nuclear weapons capability.

Haig said then that the United States had noted "some shift" in Iraq's policy, apparently caused in part by "a greater sense of concern about the behavior of Soviet imperialism in the Middle Eastern area."

The Soviet Union terminated military supplies to Baghdad after Iraq attacked Iran last September, anbd Iraq has turned increasingly to Western Europe for major arms purchases, especially to France.

Additional word of more positive Iraqi attitudes toward Washington was conveyed to Haig this week by high officials in both Jordan and Saudi Arabia, according to informed sources.

According to a well-placed Arab official, Iraq has made know its desire for:

A restoration of full U.S. diplomatic raltions, replacing the present situation in which diplomatic business is done by "interests sections" representing the two countries in one another's capitals.

"Economic cooperation," apparently including encouragement to American businessmen to sell technologically advanced equipment and a more positive U.S. attitude on licensing.

A changed U.S. attitude toward the emerging Iraqi nuclear program, which Baghdad insists is for civilian purposes but which is strongly suspected in Washington of having military motivation. In recent months U.S. diplomats have been working throughout the world to monitor and discourage sales of nuclear technology an equipment to Iraq.

A senior U.S. official familiar with the messages from Baghdad would not confirm that the first two points had been stated as unequivocally as suggested by Arab accounts. The official said no message regarding the U.S. position on nuclear issues has recently been rejected.

One reason for caution on the part of the Reagan administration Iraq's rebuff of the Carter administration in 1977 when Carter sent then-under secretary of state Philip Habib to Bagdad with a conciliatory response to what were believed to be Iraqui overtures on reestablishing relations.

In deciding to respond positively to the current signals from Baghdad, the Reagan administration took into consideration the potential effect on Iraq's national enemy, Iran, with whom Iraq has been at war since last September.

Washington views improvement in relations with Iraq as justifiable on its own merit and not as a sign of favoritism in the Iraqi-Iranian war or as any kind of statement regarding Iran, officials said.

Haig spent much of today in conversation with British Prime Minister Margaret Thatcher and Foreign Secretary Lord Carrington.