Last-minute lobbying by Vice President Mondale averted yet another setback for Carter administration legislation yesterday, as the Senate Rules Committee narrowly avoided sidetracking the President's election-day-voter-registration bill.

By a 5-to-4 vote, the committee rejected a Republican move to call Attorney General Griffin B. Bell for further testimony on a Justice Department internal memo warning that the measure had a "tremendous potential for fraud."

With Sen. James B. Allen (D-Ala.) joining the three committee Republicans in demanding Bell's testimony and four Democrats lined up against it, the swing man became Sen. Claiborne Pell (D-R.I.).

Pell was in a tough position, because Rhode Island's Democratic secretary of state, Robert F. Burns, had testified against the administration bill ast week, saying it "not only invites fraud, it makes it easy - and it makes it virtually impossible to catch anyone at it."

But a moment before the motion to call Bell came to a vote, Pell slipped out of his chair, leaving Chairman Howard W. Cannon (D-Nev.) to vote his proxy against the move.

Later, Pell said he had received "several phone calls" from Mondale and had agreed to help move the bill out of committee "even though I have no commitment to support it on the Senate floor."

The committee action left Sen. Mark O. Hatfield (R-Ore.) spluttering about a Justice Department "cover-up that has all the earmarks" of the Nixon administration scandals.

But with Pell in line, the committee appears to have an assured 5-to-4 majority to report the legislation later this week. May 15 is the deadline for reporting legislation authorizing new spending. The administration bill was reported out by the House Administration Committee on a strict partyline vote last week.

Mondale, who has been handling the legislation for the administration, had performed a similar rescue mission Tuesday on a one-vote save of the consumer agency bill in the House Government Operations Committee.

The crisis for the voter registration bill was created by Justice Department reluctance to disclose the existence of the internal memo warning of the fraud potential in Carter's proposal to permit citizens to register at their polling places on election day.

Bell made no reference to the memo when he testified before the House committee, and Deputy Attorney General peter F. Flaherty invoked executive privilege when asked about it by Republicans on the Senate committee.

Later the same day, however, the administration reversed itself and agreed to send the memo to Congress.

Anticipating a demand from Republicans that Bell be recalled for further testimony on the issue, Cannon arrived at the session with a memo from the Attorney General saying he had reviewed the internal memo, discussed it with both criminal and civil rights officials of the department.

Hatfield complained that Bell had "dismissed out of hand" the concerns about fraud expressed within his own department, and said, "I'd like to know why."

"It appears to me the Attorney general got his staff together, knocked some heads, and said here is the partyline. It smacks of a cover-up . . . What's wrong, are they afraid they will get up here and tell the truth?"

Sen. Robert P. Griffin (R-Mich.) said he understood that the U.S. attorneys in Chicago and New Orleans had also expressed concern about fraud to Flaherty and asked to see their memoranda.

But when Griffin offered a motion to seek further testimony from Bell and several other Justice Department officials, including career lawyer Craig Donsanto, the author of the internal memo, he was defeated by 5-to-4 vote.

Hatfield said that although his state of Oregon had a somewhat similar system in effect, he would fight the administration bill "tooth and nail."

However, in the markup session, the committee found bipartisan support for a move to tighten the anti-fraud provisions of the measure.

It approved an amendment offered by Sen. Dick Clark (D-Iowa) to require signed affidavits from election-day registrants attesting to their name, residence and eligibility. It would also require them to have appropriate identification or, failing that, to be vouched for by a previously registered voter. No one could vouch for more than two others, unless they were members of a family, under a provision added by Pell.