LOS ANGELES, JULY 15 -- The national effort to legalize millions of undocumented aliens by May 1988 appears to be endangered by a dispute over the role of more than 800 private agencies that help illegal immigrants apply for amnesty.

When the measure was enacted last November, the Immigration and Naturalization Service projected that 80 percent of an anticipated 1.9 million amnesty applicants would be processed initially by private agencies such as the U.S. Catholic Conference. Less than 10 percent of the 282,004 applications received through Monday have come from clients of private groups.

The system was designed to rely on preliminary processing by private agencies because federal officials anticipated that undocumented aliens would be afraid to declare their illegal status directly to the agency that, until now, has been in charge of deporting them.

Private agency officials here and in Washington now say they will need a $30 million federal appropriation and better INS guidelines to ensure that their clients meet the May 4 deadline.

The private agencies, called qualified designated entities (QDEs) in the law, charge that the INS has failed to assure immigrants that their families will be kept intact and specify what documents will be accepted as proof that an immigrant qualifies for amnesty.

Gilbert Paul Carrasco, immigration services director of the U.S. Catholic Conference, said his agency has a national backlog of 450,000 potential applicants. Most of the private agencies did not preregister amnesty applicants.

INS officials have suggested that the agencies are holding back applications to gain leverage in their policy disputes with the government. The officials also say that stricter guidelines would decrease, rather than increase, the number of people who could gain amnesty.

Los Angeles has produced more applicants than any other city. At the INS legalization office on South Soto Street in East Los Angeles on Tuesday, more than 120 immigrants filled the spacious, comfortable waiting room while 20 or 30 of them talked to legalization workers at several counters and desks.

At the legalization office run by Catholic Charities of Los Angeles at Our Lady of Victory school less than a mile away, about 25 aliens sat in small school desks on a second floor concrete balcony and waited to see four workers inside.

Katie Meskell, spokeswoman for the Catholic Charities office here, said that as of last week the organization had prepared and submitted to the INS applications for 1,200 of the 316,000 people who have sought its help to sign up for the program.

She said the group has been stymied by a shortage of volunteers and initially poor communication with the INS. When asking what documents an alien will need to prove residence in the United States since 1981, the key qualification for amnesty, the private agency staff in Washington said they often have received conflicting information.

The INS has offered to inform the group promptly if a client lacks documents, Meskell said, but still declines to provide a list.

Arthur Alvarez, chief legalization officer for East Los Angeles, one of 107 INS legalization offices in the country, said the agency would only discourage applicants if it gave precise guidelines. "Each individual case is different," he said. "A lot of people, if they truly went underground, may have no documents, so we try to find an alternative. We'll ask if they got a jaywalking ticket. At least that would prove they were here."

"If we came with a list of acceptable documents," one INS official said, "they would say we were being too bureaucratic." Some INS officials have suggested they may not need as much private assistance as they first thought.

So far, local INS offices have recommended 98.5 percent of all applications for approval, increasing the confidence of aliens who have delayed applying. Others are waiting to see what happens when those applications are reviewed at the regional level, Carrasco said.

Roger Conner, executive director of the Federation for American Immigration Reform, suggested that private agencies are critical of the application program because they had opposed the immigration reform law of which it is a part.

"There is an irony here," he said. "The same organizations that were screaming from the rooftops that INS was disorganized, unprepared and not ready to make amnesty work are now disorganized, unprepared and not ready to make amnesty work."

Anne Molgaard, regional coordinator for the Catholic Charities legalization program here, said critics did not understand the difficulties of preparing an application. She said it takes about three man-hours to fill out the lengthy forms, find and translate the necessary documents and provide photographs, fingerprints and medical certificate for each immigrant.

She said that almost all the aliens the agency has helped so far have made the requested $55 donation but that more funds are necessary. Despite startup problems, Meskell said, the Los Angeles archdiocese plans to have 22 offices processing a total of 6,100 applications a week by the end of the month.