The Carter administration proposed yesterday universal voter registration for federal elections and endorsed four other election law revised including a constitutional amendment for direct popular election of the President and Vice President.

The administration also recommended public financing of congressional elections, revisions in the public financing law for presidential elections to encourage grass-roots campaign activity, and the virtual elimination of Hatch Act restrictions on political activity by federal employees.

Unveiled at a press conference by Vice President Mondale, the proposals were endorsed by a parade of congressional leaders brought forth for the occasion.

In a five-page message to Congress, President Carter proposed a single piece legislation. It would allow every qualified voter, whether registered or not, to vote in federal elections by simply showing up at the polling place on election dday and offering proof of identity and place of residence. It would make prior registration unnecessary for voting in federal elections and would encourage states to adopt similar systems for state and local elections.

In the voter registration legislation is, in the words of House Speaker Thomas P. (Tip) O'Neill (D-Mass.), "the cornerstone" of the administration package, the biggest surprise was the President's call for a constitutional amendment to abolish the Electoral College and provide for [WORD ILLEGIBLE] popular election of the President and Vice president.

As recently as a Feb. 23 [WORD ILLEGIBLE] conference Carter said that while heiavored ending the freedom of presidential electors to ignore popular vote results in their states, he was uncertain about junking the basic concept of the Electoral College, under which all of a state's electrol votes are cast for the presidential candiadate who won the state's popular vote.

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White House [WORD ILLEGIBLE] secretary Jody powell said Carter decided to back a direct election in investment after determining [WORD ILLEGIBLE] it would probably not add greatly to the existing concentration of presidential campaigns in the heavily populated states at the expense of the small states.

In other parts of the message, Carter endorsed pending congressional efforts that would:

Provide public financing of both primary and general elections for Congress patterned after the public financing law that governed the 1976 presidential election. Carter said he hoped that public funds can be used beginning at least with the 1978 congressional general elections.

Lossen some provisions in the presidential public financing law, perhaps by allowing candidates to establish committees in each state to raise and spend funds for grass roots campaign activity there. This was in response to c riticism that existing spending limits discourage some forms of traditional local political activity.

Eliminate the Hatch Act's ban on partisan political activity by federal employees except for those in "sensitive positions" requiring them to maintain "both in appearance and th substance of impartiality."

The President's proposal for universal voter registration - one of his key campaign pledges - received an important boost on Capitol Hill when House Minority Leader John J. Rhodes (R-Ariz.) said he would support it.

Republican traditionally have opposed such voting measures, arguing that they are designed to benefit Democratic candidates would invite widespread fraud.

At his press conference, Mondale said, "There is no evidence that this operates to one party's advantage over the others."

As for fraud, Mondale added, the bill contains a tough penalty (up to a $10,000 fine or five years imprisonment, none of the states with similar simplified registration procedures has experienced a fraud problem.

In those four states - North Dakota, Wisconsin, Maine and Mondale's home state of Minnesota - voter turnout last November far exceeded the national average of 53 per cent of eligible voters, according to Mondale's office.

The administration bill would also provide about $48 million every two years to the states to help pay voter registration expenses.

Much of the congressional leadership arrayed around the vice President yesterday has also endorsed public financing of congressional elections.

In his message, the President said he would leave the specifics of such a measure to Congress. But he made a number of suggestions to model a congressional law on the presidential public financing act.

Carter's call for the elimination of the Electoral College and a drastic revision in the Hatch Act are likely to have the toughest time on Capitol Hill.

For years, Sen. Birch Bayh (D-Ind.) has been seeking passage of a constitutional amendment for the direct election of the President. Because such an amendment would require passage by two-thirds of the House and Senate and ratification by three-fourths (38) of the state legislatures, the Carter initiative is extremely unlikely to affect the 1980 presidential election.