With his supporters chanting "Four More Years," President Carter strongly defended his record last night in a preview of the kind of campaign he intends to wage against Sen. Edward M. Kennedy (D-Mass.).

Speaking to some 500 allies at a dinner, Carter said he looked forward to next year's campaign "when the American people and the news media, for a change, will accurately assess what we have fought for and achieved."

That record, he asserted, will show unsurpassed achievements by him and Congress in dealing with the nation's problems.

The dinner at the Hyatt Regency Hotel was designed as a show of political muscle by the president, who used it to needle Kennedy while defending his own record.

Poking fun at Kennedy's well-publicized "signals" of last summer concerning his intention to run, Carter said: "I asked my Mama and she said okay. Rosalynn said she'd be willing to live in the White House for four more years."

The president also issued the same indirect warning to Kennedy that he has been making for several weeks.

"I've never feared a political fight," he said. "I can say truthfully that I look forward to 1980 with anticipation and confidence."

Billed as "An Evening With Friends of President Carter and Vice President Mondale," the event amounted to the unofficial kickoff dinner of Carter's reelection campaign.

The dinner's political significance was largely in the ground rules set for it by Carter's political strategists. Those who attended were told that their presence was tantamount to an endorsement of Carter in his show-down with Kennedy for the 1980 Democratic presidental nomination.

Overall, the Carter strategists put together a generally strong show of support, attracting about 100 members of Congress, dozens of Democratic governors, mayors and other local officials, and state party leaders and political activists.

But the turnout was far from an overwhelming show of support for an incumbent president and left Kennedy with plenty of room in the Democratic Party in which to seek backers.

The dinners planners suffered one setback when Chicago Mayor Jane Byrne, who has been strongly courted by Carter, failed to appear. She attended an earlier private reception at the White House, but was quoted as telling reporters that while she supports the president, "I am not getting involved right now in any of the political aspects" of the nomination fight.

Before the president spoke, he was treated to a series of testimonials by a number of Democrats chosen to represent various elements of the party.

Los Angeles Mayor Tom Bradley said he had never known "a better team in the White House in support of the nation's cities."

Connecticut Gov. Ella T. Grasso called Carter "a governor's president," while House Majority Leader Jim Wright (D-Tex.) declared that "Jimmy Carter has brought to the White House, quietly and without fanfare, a thing called leadership."

Planning of the dinner began several weeks ago just as Kennedy was sending out the first of his "signals" that he would challenge the president for the nomination. Carter political strategtists conceived of the dinner as a vehicle to demonstrate the extent of the president's support in the face of a Kennedy challenge and to solidify and expand their network of organizational help for the coming battle.

By advertising attendance at the dinner as the equivalent of a Carter endorsement, the president's strategists also hoped to force early endorsements from Democrats who might otherwise prefer to remain officially neutral going into a Carter-Kennedy contest.

While those listed as attending the dinners included few surprises, that strategy appeared last night to have been at least partially successful, particularly from the large number of state and local officials who attended.

The president is generally credited with maintaining good relations with the nation's Democratic governors and mayors, on whom he is counting for strong support. But those officials are also the most susceptible to pressure from the White House, which enjoys the power to grant, delay or cancel federal assistance to state and local governments.

Carter demonstrated his appreciation for last night's dinner with an exceedingly rare gesture. For one of the few, if not first, times of his presidency, he attended an entire political dinner, rather than simply appearing to deliver a speech.

The Carter reelection committee also released a guest list for the dinner that included about 675 names, including at least 100 people who did not attend but were listed as Carter supporters.

The list demonstrated some of the president's strengths and weaknesses going into the expected confrontation with Kennedy. It included about 80 House members, but many were from the South, Carter's geographical base, and they included few who hold leadership positions.

Similarily, about 10 senators were listed, but they were largely from southern and border states and included none of the Senate's recognized powers.

Leaders of some labor unions attended the dinner, but many of the major unions and the leaders of the AFL-CIO were not represented.

However, the list showed strong Carter support among Democratic governors, big-city mayors and other local officials. It also showed support for the president among important elected or party officials in such key states as Iowa, New Hampshire, Florida, Texas and New York.