The Carter administration has chosen Leonel Castillo, the city comptroller of Houston, to be the first commissioner of the Immigration and Naturalization Service of Hispanic American descent, Justice Department sources confirmed yesterday.

The sources said Castillo was offered the post at a meeting yesterday with Attorney General Griffin B. Bell and is expected to accept Mario Noto, a retired INS official who had been backed for the job by Italian-American groups, is expected to be named deputy commissioner.

Castillo is one of about a dozen Hispanic-Americans chosen for major jobs in the administration. In his election campaign, Jimmy Carter promised greater representation in the government for Spanish-speaking Americans.

The INS regulates the flow of immigrants. Because its drive against illegal aliens has focused heavily on Latin America, the agency has been criticized frequently for alleged insensitivity to Hispanic-Americans.

The extent of the illegal immigration problem is not known. However, a study done for INS in 1975 estimated that there were 8 million illegal aliens in the United States, including 5 million from Mexico.

White House and Justice Department sources said Bell, who oversees INS activities, wanted a Hispanic-American to succeed outgoing Commissioner Leonard F. Chapman Jr. But, the sources added, Bell came under strong pressure from Rep. Peter W. Rodino Jr., chairman of the House Judiciary Committee, and others who wanted Noto to get the job.

According to the sources, Castillo became a serious candidate after he visited the White House in late January as part of a Mexican American delegation. White House officials reportedly were so impressed that they forwarded his name to Bell; after further investigation, he concurred in the recommendation.

However, the sources added, a final decision was delayed for several days by Rodino's continued support of Noto. After several meetings between Bell and Rodino - one of them at the White House last week - it was decided that Noto would get the deputy's spot.