President Carter has sought to reestablish full diplomatic relations with Iraq but he has found no takers in Baghdad.

The Carter administration variously justifies these efforts as a recognition of Iraq's importance as the Middle East's second biggest oil exporter, a desire to have diplomatic relations with all nations and concern about the turbulence in neighboring Iran.

Yet many foreign diplomats here think Iraq President Saddam Hussein is acting wisely in refusing to resume the links cut since the Arab-Israeli war in 1967.

It is not as if no official business is transacted between Iraq and the United States. The building flying the Belgian flag and formally known as the U.S. Interests Section of the Belgian Embassy houses more diplomats than most full-fledged embassies in Baghdad. Within its portals are conducted cultural, economic, educational and consular relations on an ever-expanding basis.

In a similar arrangement in Washington, more than a dozen Iraqi diplomats work in their country's interests section, officially part of the Embassy of India.

Indeed so much business is transacted so efficiently without official diplomatic relations that it is hard to see the advantages of formally renewing them, observers here say.

Formal diplomatic relations, it is arrgued, would only oblige Iraw to intensify its standard and deeply held criticism of the United States for its crucial support of "the Zionist entity" as the government here calls Israel.

"No formal relations at least means no demonstrations outside the embassy, no rough stuff, no embassy occupation," one diplomat reasoned.

Given the volatile nature of Middle East politics, the low silhouette of the U.S. government presence here helps avoid stiring up resentments.

Only about five years ago the United States and Israel were supporting a full-fledged Kurdish rebellion against the Baghdad authorities.

In the current border tension between Iran and Iraq, both countries have accused the United States of varying degrees of involvement.

Recurring rumors, sometimes published in newspapers in the nearby Persian Gulf states suggesting that Saddam Hussein has accepted an invitation to Washington or has met high U.S. officials on the Iraqi-Jordanian border, are written off here as Iranian-inspired propaganda. i

Major powers like the United States often find advantages in the approach of nonrecognition. During the Vietnam War, for example, the United States had no diplomatic relations with Algeria, but operated an interests section in Algiers that handled a considerable volume of trade.

Both governments realized formal diplomatic relations were impractical in light of Algeria's identification with the North Vietnamese and Vietcong in their flight against the United States.

Here U.S. consular staff issue visas for Iraqis, including a growing number of university students encouraged by Iraqi government policy and scholarships to study science and technology in the United States.

Whatever Iraq thinks about Carter's Middle East policy, it makes little secret of its admiration of and desire to acquire American technology. This desire is so deep-seated that U.S. congressional and executive reluctance to provide the latest gadgets is interpreted here as a combination of Israeli pressure and a deliberate effort to prevent an emerging nation from narrowing the technology gap.

Thus, many diplomats feel Washington should leave well enough alone.

"The Americans have only slightly less contact with Iraqi officials than most missions here," a European envoy said, lamenting the extremely circumscribed life of diplomats here.

"Most Iraqis are scared to accept our invitations," he said, "and we need hard-to-get permission to go anywhere outside Baghdad except Lake Habbaniyah," a resort about an hour's drive from the capital.

"So with the whole diplomatic corps pretty much cut off, why bother?" remarks another envoy. "Elevating relations in America's case would just elevate the level of the snub. And this way the American charge d'affaires doesn't have to go to the airport every time there's a visiting head of state. And that's a major blessing."