Democrats yesterday beat back a series of Republican attempts to undermine President Carter's proposal allowing registration of voters on election day.

The actions came in the House Administration Committee on amendments offered by Reps. Charles H. Wiggins (R-Calif.) and William Frenzel (R-Minn.). However, Committee Chairman Frank Thompson Jr. (D-N.J.) made one concession to the GOP when he proposed an amendment, which was accepted unanimously, that would allow at least 16 states to put off same-day registration until 1980.

The delay would be allowed states whose legislatures will not convene in a scheduled general session before next March 31.

An amendment by Frenzel that would have made the legislation entirely voluntary in the 1978 elections was defeated 15 to 10 when Thompson cast 10 Democratic proxy votes against it. Two of the seven Democrats present voted with Republicans for the amendment, and Frenzel said he would bring it up again on the House floor.

"I think it has a fair chance to pass on the floor," Frenzel said. "The Congress is going to hear from the home folks who run the elections and are worried about having enough start-up time."

The committee turned down another amendment by Frenzel that would have extended the same-day registration requirement to primary elections, in which even fewer voters participate than general elections. Many of the Democrats appeared to favor this amendment but questioned whether the legislation would pass if it were accepted.

And on a straight party-line vote the committee turned down an amendment by Wiggins that would have limited election-day registration to primaries only.

"To the degree we're going to practice fraud, let's practice it on each other in our parties," said Wiggins.

Thompson has rejected the frequent contention of Republican members and of Chicago witnesses, mostly Democrats, who say the legislation would encourage fraud.

The committee expects to complete deliberations this week and vote on the amended bill. Still at issue is the thorny question about how much information should be asked of the citizen who files an affidavit on election day declaring he is legally qualified to vote.

The Senate opens three days of hearings on the bill today.