Sen. Mark Hatfield of Oregon, prospective Republican chairman of the Senate Appropriations Committee, said yesterday he is pressing President-elect Reagan to wipe draft registration off the books.

In discussions with Martin Anderson, Reagan's domestic policy coordinator, Hatfield said, he has argued for action that would suspend the present requirement that men born in 1962 register at their local post offices in the first week of January.

If Reagan were to tell President Carter that he intended to cancel draft registration upon taking office, Carter might suspend the January registration order, saving $5 million in the process, Hatfield said.

"We're hopeful" that this course will be followed, Hatfield said, adding, "The receptivity is very warm" by Anderson.

Hatfield earlier this year attempted to stop draft registration by filibustering against the bill to finance it. Congress ended up providing the necessary money, while Carter, by executive order, directed all males born in 1960 and 1961 to fill out forms at their local post offices this past summer in case the draft were reinstituted.

The Committee Against Registration and the Draft has been circulating the anti-registration views of Reagan as part of its campaign. On May 5, 1980, Reagan wrote Hatfield that the Carter administration's effort to bring back registration "is an ill-considered one and should be rejected. Advanced registration will do little to enhance our military preparedness."

"Instead," continued Reagan in his letter, "our national security demands an adequate reserve that can be called up at a moment's notice, and a skilled, experienced, all-volunteer force that can handle sophisticated equipment.

"Perhaps the most fundamental objection to draft registration is moral. Only in the most severe national emergecy does the government have a claim to the mandatory service of its young people. In any other time, a draft or draft registration destroys the very values that our society is committed to defending."