President Carter yesterday exhorted Congress to enact several key pieces of legislation during the closing days of this session, but warned that the Senate bill that would cut taxes by more than $29 billion is "unacceptable" and will be vetoed unless changed.

Carter began a nationally televised news conference by calling for enactment of "a fair tax bill," the Humphrey-Hawkins "full employment," legislation and, most important, he said, the natural gas deregulation portion of his energy program, which faces a final House test later this week.

The Senate took up the Humphrey. Hawkins bill last night, and is to continue the debate today.

On tax legislation, the president said that a $16.3 billion tax cut measure passed by the House "is within the guidelines that I have established" and "would not be excessively inflationary." But the Senate bill, he added, "would not be satisfactory in its present form."

"My hope is that the House and the Senate conferees over the next two or three days can reach an agreement, extracting the most acceptable elements from the House bill, combining them with the most acceptable elements of the Senate bill so that I can sign the final bill as passed," Carter said.

"If not," he continued, "then there will be no tax bill this year, because I will veto it. The only option would be for the Senate and the House to come back in a special session after the election, which I would not favor personally."

The president's comments marked a last-minute attempt by the White House to influence the enactment of "acceptable" tax legislation.

Carter initially proposed legislation that he said contained major elements of "tax reform" and a net tax cut of $25 billion. The House eliminated most of the "reform" provisions and eventually slashed the size of the cut to $16.3 billion, a reduction the administration accepted to counter growing worries over inflation.

The Senate, however, has gone in the opposite direction, swelling the size of the proposed tax cut to almost $30 billion, just as the president is about to announce what he has called a "tough" new anti-inflation program.

The president is to discuss the differences in the two bills today in a meeting with Senate Finance Committee Chairman Russell B. Long (D-La.), House Ways and Means Committee Chairman Al Ullman (D-Ore.) and Treasury Secretary W. Michael Blumenthal.

On Monday, the Senate also enacted a Democratic version of the Republican Roth-Kemp bill that would cut income taxes by $142 billion from 1980 through 1983 if the government meets stringent targets for holding down federal spending.

Asked about this at the news conference. Carter suggested that he does not expect the proposal to survive in the House-Senate conference committee deliberations on the final shape of tax legislation.

It would be very difficult to consummate as far-reaching and as controversial and as innovative concept as that in the last few hours of a congressional session," he said.

The president's decision to open the news conference with plugs for the Humphrey-Hawkins and natural gas bills reflected both pressure on him and a fear in the White House that, after an almost two-year struggle Congress still might fail to enact significant national energy legislation.

The Congressional Black Caucus has been pressing Carter for more intensive support of the Humphrey-Hawkins legislation, which would set a goal of reducing the overall unemployment rate to 4 percent by 1983. Yesterday, the president responded, declaring at the start of the news conference that "the passage of this legislation [is] very greatly needed . . ."

The bill is scheduled to come up in the Senate today.

Some officials have questioned the extent of the administration's devotion to the Humphrey-Hawkins bill, but there has never been any question of Carter's commitment to the natural gas bill, the fate of which, he said yesterday, will determine the congressional record for this year.

"I believe that this vote is the most important that will be cast by the members of Congress during this year," he said. "And it will be a measure of our government and also a measure of achievement for the year."

On other domestic topics, the president confirmed that he will not announce new anti-inflation measures until after Congress has completed its current session, and he conceded that Congress is not likely to enact administration legislation creating a separate department of education.