President Reagan, after hearing his deputies' arguments for and against keeping draft registration on the books, went home for Christmas without deciding the question, administration officials said yesterday.

Defense Secretary Caspar W. Weinberger, during part of a National Security Council meeting at the White House last Friday, argued against scrapping the requirement that 18-year-olds must register for the draft.

Sources said Weinberger contended at the White House meeting that such a move would send the wrong signal to friends and foes alike about the determination of the United States to shore up its military strength.

Martin Anderson, assistant to the president for policy development, represented the other pole of the argument at the White House session, according to informed officials. He long has philosophically opposed either registration or conscription in peacetime.

"The passage of a draft registration law," wrote Anderson last year in explaining his opposition, "will only give a false sense of security to our people and to many of our political leaders. It will be used as a reason by some and an excuse by others for not taking the hard steps that will strengthen our reserve forces to the point that they can actively back up our active forces."

Reagan, as a presidential candidate, took a similar stance. On May 5, 1980, he wrote Sen. Mark Hatfield ((R-Ore.), a member (and now chairman) of the Senate Appropriations Committee that "the most fundamental objection to draft registration is moral. Only in the most severe national emergency does the government have a claim to the mandatory service of its young people."

Since draft registration was ordered late in 1980, more than 800,000 young men have failed to register, despite the risk of being fined up to $10,000 and being jailed for five years. Earlier this month the Justice Department ordered its attorneys to suspend prosecution of violators until Reagan had decided whether to continue the registration requirement.

At the National Security Council meeting of last Friday, Justice confined itself to discussing the legal implications of enforcing the registration law and did not push for either keeping or scrapping it, officials said.