The U.S. Court of Appeals said yesterday that the Carter administration could resume its search for Iranians who are in this country illegally, but continued a ban on deportations until the constitutionality of the administration's actions can be reviewed at a hearing next Thursday.

The order by two appeals court judges came in response to a ruling on Tuesday that President Carter's crackdown on Iranians was illegal because is targeted a single group of aliens.

The government immediately took the decision by Judge Joyce Hens Green to the appeals court, which agreed yesterday to hear the case on Dec. 20. In the meantime, the appeals court said, Immigration and Naturalization Service officials could continue to interview Iranian students and review their status in this country but could not deport them.

In its filing with the appeals court, the administration said it would not enforce any deportation orders that may have resulted from those interviews until the case is resolved. Attorney General Benjamin Civiletti also agreed to extend to Dec. 29 the deadline by which Iranian students here are to report to their nearest INS office, a Justice Department spokesman said. The original deadline was yesterday.

Judges George E. MacKinnon and Roger Robb issued the order for the appeals court yesterday.

The Justice Department, in papers submitted to the appeals court, repeated its argument that the deportation regulations issued Nov. 13 were in response to the unlawful detention of 50 American hostages at the U.S. Embassy in Tehran.

The president's directive to identify Iranian students who are here illegally was "one step in a carefully measured series of actions taken to alleviate that situation" and to secure the safety and release of the hostages in Iran, the government said in court papers.

Judge Green's decision to strike down the regulations had the effect of negating "the diplomatic message it conveyed (and did) harm to the president's foreign policy efforts," the court papers said.

In comparison, the government argued, the Iranian students are required by the regulations only to make a minor adjustment in their schedules -- the visit to the INS office. Many of those interviews have taken place on college campuses, the government said.

The government urged the appeals panel to consider the administrative difficulties and expense that would occur if the reporting process was "stopped in its tracks" while the question of the constitutionality of the entire procedure is argued.

Judge Green's decision came in response to two lawsuits filed by Iranian students here backed by the American Civil Liberties Union, the National Emergency Civil Liberties Committee and the Socialist Workers Party.

The appeals court had to determine which side of the case would suffer the greatest harm if the effectiveness of Green's order was postponed until the appeal was decided.

A Justice Department spokesman said yesterday that 53,006 Iranians had been interviewed by Tuesday, when Green's order was issued. Of that number 43,509 persons were found to be in compliance with INS regulations and another 6,255 were in violation and could be deported the spokesman said. Of the persons interviewed, 47 have applied for asylum in the United States, 823 were permitted to leave the country voluntarily, and 10 Iranians have been deported, the spokesman said.