A House committee yesterday approved President Carter's election-day voter registration plan less than an hour after the Justice Department made public an internal memo describing the legislation as creating "a tremendous potential for fraud."

The bill cleared the House Administration Committee on a 17-to-8 vote with all the Democratic members voting for it and all the Republicans against. The partisan division reflects a widespread belief on the commitee that the bill will politically benefit the Democrats.

Despite the victory in committee, Democrats were embarrassed by the timing of the Justice Department memo. Written by Craig Donsanto, a career attorney who heads the election unit within the Criminal Division, the memo contended that pre-registration of at least 30 days was necessary to detect the common types of vote fraud.

The memo points out that the signatures usually made on voter registration cards were the principal basis of detecting voter fraud in Chicago and, more recently, in Louisiana, where a number of election officials have pleaded guilty to forging the signatures of "no-show" voters.

"The requirement that persons seeking to vote without prior registration produce some form of identification . . . at the polls is essentially meaningless," the memor said.

The memor was withheld Wednesday from the Senate Rules Committee by Deputy Attorney General Peter F. Flaherty on grounds of "executive privilege." This doctrine has an unsavory connotation to many Democratic congressmen, who associate it with former President Nixon.

House Administration Committee Chairman Frank Thompson Jr. (D-N.J.) saw a wire service account of Flaherty's testimony and called Vice President Mondale, who moved swiftly to undo the damage.

"Pete and I agreed that the memo ought to be released immediately," the Vice President said after a telephone call to Flaherty.

Copies arrived yesterday at the House Administration and Senate Rules committees with a cover letter from Flaherty reaffirming his support and that of Attorney General Griffin B. Bell for the legislation.

During a week of deliberations, the House committee aded a number of amendments aimed at providing safeguards against fraud.

An amendment aded yesterday would strengthen the investigatory powers of the Federal Election Commission in civil violations of the law. Another amendment would require a post-election audit of at least 5 per cent of the voters or precincts to check on fraud.

Earlier, the committee required that individuals registering on election day file an affidavit under penalty of perjury listing their age, residence and date and place of birth.

Democratic supporters of the bill say that these provisions, and the criminal penalty of up to five years in prison for willful fraud, will discourage abuses. Republican opponents - and Chicago officials of both parties - say that it will be almost impossible to locate someone who registers fictiously on election day and votes.

This is the view of the Justice Department memo, which said the bill amounts to "a dangerous relaxation of what precious few safeguards presently exist against abuse of the franchise."

Thompson, who acknowledged that the legislation would work to the general advantage of Democrats, predicted that the bill would be approved overwhelmingly by the House. He said, however, that there was "a 50-50 chance" that the House would accept an amendment by Rep. Bill Frenzel (R-Minn.) making election-day registration voluntary for states in the 1978 elections.

The bill may face a stiffer test in the Senate, where the Rules Committee continued hearings yesterday. The committee will begin markup next week.

Chairman Howard W. Cannon (D-Nev.) observed yesterday that "there is a lot of opposition from people who deal with this at the state level."