The Reagan administration has warned Congress that a Senate plan to grant amnesty to millions of illegal aliens could cost more than $10 billion in new state and federal welfare costs over the next four years.

"At a time when we are facing necessary cutbacks in welfare programs for our citizens, such extraordinary added costs to provide benefits to former illegal aliens cannot be justified," Attorney General William French Smith wrote in a July 11 letter to Sen. Strom Thurmond (R-S.C.), chairman of the Senate Judiciary Committee.

The bill's sponsor, Sen. Alan K. Simpson (R-Wyo.), called the figures "seriously distorted." And Arnold Torres, executive director of the League of United Latin American Citizens (LULAC), accused Smith of exaggerating costs to "scare the public and the Congress."

Under the sweeping immigration reform bill approved by the Judiciary Committee, 4.8 million illegal aliens are estimated to be eligible for amnesty. About 1.2 million who arrived in the country before 1978 would become permanent residents and thus eligible for the major federal benefit programs.

The 3.6 million who arrived before Jan. 1, 1982, would become temporary residents, eligible for only a few benefits. But they would become permanent residents within two years.

The House version of the bill limits the entry date for amnesty to 1980, and thus covers 2.7 million aliens. Simpson said that Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) had promised that the bill would be brought to the Senate floor before the Labor Day recess. It also includes controversial provisions to make it illegal to hire undocumented aliens.

In the letter, Smith called the Senate bill's legalization terms "precipitous and unwise" and said he feared it would encourage more illegal migration. He suggested a "more gradual and much less costly" $1 billion alternative.

He also criticized as unconstitutional the bill's plan for a counterfeit-proof identifier to enforce sanctions against employers who hire undocumented workers.

LULAC's Torres said the administration's $10 billion figure--$6.3 billion in federal and $3.9 billion in state and local costs--ignores the provision in the bill that requires legalized aliens to show they won't be "public charges."

Simpson said in a telephone interview that the administration figures were "seriously distorted" because they assumed the legalized aliens would use welfare and other social services at the same high rate as refugees. About 71 percent of the refugees are dependent on government social services, he said.

"What we say to them is, good heavens, the people we are talking about are illegal, undocumented workers, mostly young, mostly single, who came here for one reason: to get a job," Simpson said. "They are working."

The report accompanying the Senate bill used Congressional Budget Office figures that estimated that the legalized aliens would not use the welfare system any more than the general population. Simpson said the administration is unhappy with the legalization provision "so they are using the ancient game of numbers."

David D. Hiller, an associate deputy attorney general who works closely with Smith on the immigration issue, said Friday the administration's figures were "prudent and plausible" but in the upper range of probability.

He said the $10 billion cost estimate assumed that 80 percent of 6 million illegal aliens would take part in the amnesty program.

"The welfare costs could be substantially below the costs in the letter," he said. "But for planning purposes we felt we had to be conservative. . . . The numbers were not deliberately contrived to be scary."

Hiller said the administration agrees with the claim that most illegal aliens are working, but he suggested that some aliens might quit their low-paying jobs if they were eligible for welfare.

"Human nature being what it is, if programs offer free goods and services, a lot of people might accept them," he said.

Smith's letter to Thurmond suggested that the bill be amended to offer permanent resident status to aliens who entered the country before 1976. This would cut the number eligible for most benefit programs to 600,000. He also proposed making temporary residents wait four years, rather than two, to become eligible for full benefits as permanent residents.