Vice President Mondale, bearing a message of conciliation for the supporters of Sen. Edward M. Kennedy, arrived here today and immediately began trying to focus attention on the "gulf" separating all Democrats from Ronald Reagan.

While President Carter remained in the seclusion of Camp David, Mondale took over the public role of leader of the Carter forces at the Democratic National Convention in a series of appearances before statee delegations.

His aides and other Carter strategists remained supremely confident they will win the fight Monday night on the convention rule binding delegates to vote for the candidate they were elected to support.

They were less confident, but hopeful, that the convention will then end Thursday night with a show of unity and reconciliation between the president and his challenger.

Carter aides insisted they were doing everything necessary in the negotiations with the Massachusetts senator's campaign to assure such a show of reconciliation comes about. But they conceded that while they may control the convention proceedings inside Madison Square Garden, it is Kennedy who will have the final say on how it all ends.

"If he wants to find some reason to go to Hyannisport [before the convention's end], he'll be able to find it," said one Mondale aide. "If he wants to accommodate, stay here and talk about Ronald Reagan, it will be no problem."

It was this job of patching up the differences that divide the Carter and Kennedy supporters that was the vice president's first task after arriving here.

At a news conference, Mondale said he hoped that Kennedy "will find it possible to support this ticket.

"I know the senator is well aware of Mr. Reagan and his policies and the disastrous consequences they would have. They would undermine and destroy everything we have fought for. Everything we have fought for is at risk in a Reagan presidency."

A longtime liberal ally of Kennedy in the Senate, Mondale represents a potentially critical bridge between the two campaigns, and as he made the rounds today among Carter supporters his message was the same -- forget the bitterness of the primaries and turn your attention to the Republican nominee.

"What differences might divide us monentarily, they are nothing compared with the gulf between the Democratic Party and the Republican Party of Ronald Reagan," he told members of the National Education Association, a key Carter support group.

Kennedy is scheduled to address the convention Tuesday night during the platform debate when. Carter aides fear, the deep anti-Kennedy emotions of many of the president's supporters could erupt, complicating the task of reconciliation. So today, while he gave the Carter delegates a final pep talk before the rules fight, Mondale also urged on them a code of good behavior.

"Let's have our debate, but let's keep it civilized," he said. "Let's have disagreements, but keep it under control. We are not each other's enemies."

Besides Kennedy, it was Reagan who was most on the vice president's mind as he sounded some of the themes the Carter campaign is expected to use in the fall.

While Carter is experienced and a "gifted" president, Reagan has no experience, has demonstrated "little or no knowledge of foreign affairs" and has a "tendency to think America can somehow shoot itself into peace."

To the education association members, he said of Reagan: "That man should not be president of the United States. And we're going to see to it together that he isn't."

With this city jammed with high-ranking White House and administration officials, there was only one prominent absentee on the eve of the convention's opening -- the president.

But Carter made an electronic appearance to the convention and the nation in an interview tonight on the television program "60 Minutes" (CBS, WDVM), during which he, too, sounded themes for a fall campaign.

The president said he believes there are even sharper differences between him and Reagan than there were in 1964 between Democratic President Johnson and Republican nominee Barry Goldwater.

He said he hopes to have several debates with Reagan and added, for the first time without qualification, that he is willing to participate in a "debate" involving not only Reagan but independent presidential candidate John B. Anderson.

But Carter also criticized Anderson as "a freewheeling agent [who] can change positions as he sees fit" and who is viewed by many as a politician "who abandoned his own party."

In the interview, which was conducted Friday at the White House, the president said he would like his brother, Billy, to return the $220,000 in payments he received from Libya. Carter, however, shed no new light on the Billy Carter controversy.

The president is scheduled to remain at Camp David until Wednesday, when he will travel here for the roll call on the Democratic presidential nomination.