Despite objections from some members of Congress, the State Department announced Thursday that it had approved the sale of eight U.S.-built gas turbine engines meant to power four Iraqi warships being built in Italy.

Congressional objections to the sale were based on claims that the original license by the Commerce Department had been approved last January without prior notification of Congress. Furthermore, critics said the sale violates a law requiring such notification when military equipment is sold to countries that are found to have supported international terrorism.

Reps. Millicent Fenwick (R-N.J.) and Jonathan Bingham (D.-N.Y.) of the House Foreign Affairs Committee wrote to President Carter in February expressing "deep concern" over the license approval and calling it "an apparent violation of the Export Administration Act of 1979."

The letter pointed out that Iraq, along with Libya, Syria and South Yemen, was on the terrorism-supporters list that accompanied President Carter's letter of last Dec. 29 to Congress on export controls.

After the February protest, the State Department agreed to delay the sale and review the decision.

On Thursday, however, it became clear that the matter was now final as far as the Carter administration is concerned. In a brief statement in response to reporters' inquiries, the State Department said:

"The decision to grant an export license, made in January, has been carefully reviewed in light of the concerns expressed in Congress about the sale. We concluded that it would not be in our overall foreign policy interest to revoke this export license. We continue to keep in touch with Congress on this issue."

The administration had previously contended that ship engines were not on the list of items supposed to be withheld. But the new explanation makes it clear that foreign policy interests are paramount.

Since the fall of the shah's regime in Iran, Iraq, with its heavily armed military, looms as the most powerful state in the region. And, while the United States does not have formal diplomatic relations with the Baghdad regime, informal relations have been improving as Iraqi ties to Moscow weaken.

Israel has also strongly opposed the sale. Members of Congress say they received information from the administration calling such engine sales routine on the same day this year that the State Department identified those who raided a small Israel settlement and killed several people as an Iraqi-backed Palestinian group.

The sale involves jet-style engines built by General Electric Co. in a contract valued at $11.2 million.