A key Roman Catholic Church official has called on the federal government to extend the May 4 application deadline for illegal aliens to seek legal status in the United States.

Archbishop Theodore McCarrick of Newark, chairman of the U.S. Catholic Conference's Committee on Migration, said Thursday that enforcement of the deadline will leave "a large residual alien population" in the United States "forced to live in fear of deportation, unable to procure employment" and without access "to critical social services, creating a dispossessed, disenfranchised underclass subsisting on the edge of society."

The Catholic Church has played a central role in the debate over the Immigration and Control Act and in promoting the legalization program.

Urging the government to extend the deadline under which undocumented aliens may apply for legal status, McCarrick cited a study released last week by the Carnegie Endowment for International Peace that concluded: "Even if an additional 300,000 to 400,000 applicants could be reached {by May 4}, the size of the remaining illegal population in the country would be almost twice the number who have been legalized."

McCarrick said in a statement that the Catholic Church "is deeply concerned about the undocumented living in our midst," adding, "We must now ask what can be done to ensure that the goals of this program {of legalization} are truly realized."

In addition to extending the application deadline beyond May 4, McCarrick said the Catholic conference, the social policy arm of the bishops, "highly recommends" provisions that would qualify more people for legalization.

Any extension bill considered by Congress, he said, should give more generous assurances to families with both eligible and ineligible members, lower the cost of applications, relax the limitations on absences from the continuing residency requirement and ease the demands for documentation.

McCarrick also recommended that the eligibility date be advanced to Nov. 6, 1986, to address the plight of those who entered the United States illegally after 1982.