President Carter proposed yesterday that all men born in 1960 or 1961 be required to register for the military draft later this year and said he will ask Congress for authority to require women born in the same years to register.

In future years, all men -- and women if Congress votes to include them -- would be required to register for the draft as they reach their 18th birthday, according to the plan.

The registration would be accomplished through the Postal Service. Young people would be required to go to their local Post Office and fill out a form with their name, address, date of birth and, at their option, their Social Security number.

The information would be stored in Selective Service System computers. Draft cards would not be issued, and there would be no physical examination or classification by marital or other status of the registrants.

The president's decision, part of his response to the Soviet Union's invasion of Afghanistan, is expected to set off sharp congressional debate about both the prospect of reviving military conscription and the possibility of requiring American women to serve in the military for the first time in history.

In a written statement issued yesterday after he had left Washington for Camp David, Carter said he had no choice but to call for the inclusion of women in the registration system.

"There is no distinction possible, on the basis of ability or performance, that would allow me to exclude women from an obligation to register," he said.

But the president also proposed continuation of the tradition that women in the military serve in noncombat roles, although White House officials said an effort will be made to broaden the definition of noncombat functions so that women are not needlessly denied promotions.

White House officials acknowledged that there is strong opposition in Congress to registering women, and that this may doom Carter's proposal. But any attempt to require men to register while excluding women is also expected to provoke equal rights lawsuits that could force female registration. e

The president asked Congress to appropriate $24.5 million this year that begins Oct. 1 to put the registration machinery into place. Officials said some appropriation by Congress will be necessary even to register men, and it is over the funding that the congressional battle on whether to resume registration will be fought.

The call for registration drew immediate fire yesterday. Sen. Mark O. Hatfield (R-Ore.) said the plan "will deeply divide the country at exactly the time we need solidarity," while Barry W. Lynn, head of an antidraft coalition of 42 organizations, said resumption of any registration will only feed "war hysteria."

As described by White House officials, the registration system the president plans would work this way:

The initial pool of registrants would come from 19 and 20-year-old men, who number 4 million, and -- if they are included -- 19 and 20 year-old-women, another 4 million.

However, the key factor in determining who would be included in this initial pool is not a young person's age now but whether he or she was born in 1960 or 1961. Thus, 20-year-olds who were born in 1959 and will turn 21 this year would not be required to register.

Beginning next year, young people born in 1962 would be brought into the system as the routine registration of 18-year-olds begins.

Those required to register including the initial pool formed this year, would remain eligible to be drafted through age 26.

White House officials said the registration could not begin until after Congress appropriates the additional funds, probably sometime this summer.

The prospect that Congress will vote to include women in the system appeared dim yesterday. "I'm sure he realizes it will not pass," said Rep. Richard C. White (D-Tex.), chairman of the House Armed Services manpower subcommittee, which would have to approve legislation authorizing the registration of women.

However, Stuart E. Eizenstat, Carter's chief domestic policy adviser, said that even if Congress rejects the legislation dealing with women, the White House will seek funds to register men only.

Stressing that the president does not comtemplate the resumption of conscription, Eizenstat said the renewal of registration "will send a strong message to the Soviet Union that this country is resolved to do what is necessary in the long run to meets its agression."

He said the issue of registering women was discussed with the leaders of numerous women's groups. While these women were divided on the question of any kind of registration, Eizenstat said, "the vast majority felt that if it is necessary for men to register, it ought to be necessary for women."

Justifying his decision to call for registration of women, the president said, in his written statement:

"My decision to register women is a recognition of the reality that both men and women are working members of our society. It confirms what is already obvious throughout our society -- that women are now providing all types of skills in every profession. The military should be no exception."

Just as we are asking men to assume additional responsibilities, it is more urgent than ever that the women in America have full and equal rights under the Constitution," he added, in a call for ratification of the Equal Rights Amendment. "Equal obligations deserve equal rights."

Carter also argued that reestablishing registration now would save critical time if resumption of the draft for a military mobilization became necessary. Eizenstat estimated the time savings at several weeks at the least, a point that is disputed by draft critics.

Eizenstat also acknowledged that in restricting the initial pool to young people born in 1960 or 1961, rather than including all 18 to 26-year-olds, the president's plan would allow millions of young people to escape the requirement to register.

But he said making the pool any larger at first would be needlessly costly and cumbersome, and that the military services prefer people in the 18-to-20-year-old bracket because they tend to be in better physical shape and are less likely to have careers and families than older men and women.