After nearly a week of debate the Senate yesterday approved, 58 to 34, the $13.3 million needed to register 19- and 20-year-old men this summer for a possible military draft.

The bill must go back to the House, which approved it in April by a 30-vote margin, because the Senate made a minor change in the money figure. Final House approval is expected to send it to the president early next week.

Assuming the bill is enacted next week and is not held up in court, the administration plans a two-week registration program at local post offices in the latter part of July. Young men born in 1960 would register one week. Those born in 1961 would sign up in the other week. Congress rejected proposals to register young women.

Registration involves listing name, age, address and telephone and Social Security numbers. The cards would be sent to the Selective Service System to become part of a computerized list. If a registrant moved, he would be required to send is his new address. Failure to register could subject a person to a five-year prison term and a $10,000 fine.

Neither the bill nor existing law provides for anything beyond registration.

No legal authority exists for the government to classify those who register or to draft young people into military service. There can be nothing but a list of names unless Congress passes more legislation.

Even so, the American Civil Liberties Union said yesterday it plans to challenge the registration provisions as unconstitutional as soon as the bill is signed and to ask a federal district court here to throw them out as discriminatory because only men are covered.

The ACLU said it will go into court at first opportunity -- perhaps as early as Monday -- with a class action suit on behalf of young men age 19 and 20. A spokesman said the ACLU has at least a dozen young men as complainants. If the ACLU is successful, it could block registration until a new law applying to both men and women is enacted.

Sen. Mark Hatfield (R-Ore.) led a filibuster on the registration bill that lasted nearly a week and kept the Senate in session for nearly 33 hours straight from Tuesday morning to Wednesday evening, but the issue was not close. Hatfield could have kept talking until Saturday under a Senate rule that provides for 100 hours of debate after cloture has been invoked. But he chose not to.

President Carter asked for funds for registration -- he already had the authority -- as evidence of American resolve after the Soviet Union invaded Afghanistan last December. But opponents contended registration would be a meaningless gesture. It would not solve the defense establishment's serious manpower problems, they argued, and is bound to stir dissent that may send many young men to prison.

"Young people want to know what they're signing up for," said Hatfield.

Opponents contend that registration makes no sense unless it is viewed as a first step toward reactivating the military draft, which they oppose in peacetime. President Carter and House leaders have said there is no intention to seek authority to draft young men into military service unless there is a crisis. But several leading senators favor a draft and frankly said they hope it will be reactivated soon. They argue that the all-volunteer system is not providing the caliber of people needed to operate a modern military machine.

Hatfield and other opponents agreed to quit filibustering Wednesday in exchange for a promise that they would be given one last chance to cut the funds to a point that would make registration impossible.

The amendment offered by Hatfield would have reduced the money from $13.3 million to $4.7 million. This would have permitted the administration to get its computers ready to handle registration lists after mobilization had been ordered, but would not have been enough to permit registration. Hatfield lost, 35 to 59. Both Maryland senators voted with Hatfield. Both Virginia senators voted against him.

On final passage, both Virginia senators voted for the bill. Both Maryland senators voted against it.