President Carter emerged from the seclusion of his Georgia vacation today, renewed his assault on Ronald Reagan's "inflationary" tax proposals and challenged the Republican presidential nominee to meet him in a series of debates in the fall.

The debate challenge, which was immediately accepted, was made by Carter in a telephone call this morning to Reagan at the Republican convention in Detroit. White House officials also released the text of a telegram the president sent to Reagan today in which Carter congratulated the former California governor on his victory and said he looked forward to "a hard fought and thoughtful campaign" on the "serious choices" facing American voters.

A few hours after the congratulatory message had been dispatched to Detroit, the president fired the first shots of the fall campaign, with a swipe at Reagan's call for a federal income tax cut to stimulate the economy.

In response to questions before a group of community leaders here, Carter suggested as he has before that he will propose a tax cut next year, but said that for this year, "we will stand firm, hold a steady course, on economics.

"It is not easy in an election year, because it is too easy to promise magic answers from tax cuts," he continued. "This has been proposed by some, but I will not do that until I am sure that we are in control of inflation and until I am sure that the federal government has exercised proper discipline in setting an example for the rest of the nation."

Mentioning Reagan by name for the first time, the president said in response to another question:

"We've still got a basic [inflation] rate that's too high. But I don't believe that we ought to panic . . . I think Gov. Reagan has proposed a 30 percent cut in federal income taxes ove r a three-year period. That's $280 billion by the year 1985. The shock of that and all that flood of extra money coming into the economy, I think, would restimulate the inflationary spiral in a devastating way."

Tonight at a Democratic Party fundraiser in Hollywood, Fla., Carter sounded a partisan note but steered clear of specific references to Reagan.

He told about 600 Democrats who paid $1,000 a couple to attend the event that in the fall campaign they will face "a party that is almost the opposite of ours."

The GOP, Carter said, is "a party with a narrow vision, a party that is afraid of the future, a party whose leaders are inclined to shoot from the hip, a party that has never been willing to put its investment in human beings who are below them in economic and social status."

After five days of relaxation and fishing on Sapelo Island, Ga., Carter chose today -- the day of Reagan's final triumph at the Republican National Convention -- to emerge into the open with campaign and fund-raising appearances here and in Hollywood.

The message the president delivered to the friendly crowds that greeted him was distinctly conservative, stressing his commitment to higher defense spending, which Reagan and the Republicans are also making a main theme of their fall campaign.

At a noontime rally outside the state office building here, Carter also told the crowd he shared its belief in the value of hard work. "We don't believe in a free lunch, he said.

Florida was a keystone of the solid southern base on which Carter built his victory in 1976. But like other conservative southern states, Florida cannot be taken for granted this year by the president as he faces the conservative challenge from Reagan.

There were few details available about Carter's debate challenge or his telephone conversation with Reagan, which took place at 9:30 this morning.

In Detroit, Reagan said he looks forward eagerly to debating the president but he did not go into specifics.

Carter's willingness to debate Reagan was not surprising. Like his predecessor, former president Ford who challenged him to debate in 1976, Carter trails his challenger in public opinion polls and faces a tough reelection campaign. It is also an article of faith among his political advisers that the president's grasp of the details of government will make him a decisive winner over the GOP nominee in their head-to-head confrontations.

Carter's anxiousness to debate Reagan was evident in the telegram he sent to his opponent. In it, he suggested as many as four televised encounters rather than three, which has been the case in the previous series of presidential debates.

In order to clarify the issues between them, the president said in the telegram, "I suggest that we meet in a series of debates in the various regions of our nation. I would hope that at least three or four debates can be scheduled so that we can thoroughly discuss issues of national concern and of interest to the people of particular sections of our nation."

Left undecided was the question of whether independent presidential candidate John B. Anderson would be invited to participate in any of the Carter-Reagan debates. The president initially said he would not debate Anderson, but after that provoked wide-spread public criticism, he backed down and suggested he might be willing to share a platform with Anderson.

White House deputy press secretary Rex Granum said Carter's debate proposal today concerned only him and Reagan but that the president might still be willing to make other appearances with Anderson.

Reagan, meanwhile, reaffirmed his receptiveness to having Anderson included in the debates, saying:

"Well, if he [Anderson] collects enough of the electorate that the League of Women Voters think he's a viable enough candidate to be in the debates, that's all right with me."

The League of Women Voters, sponsor of the 1976 presidential debates, is currently trying to decide whether to invite Anderson to the debates this year.

Except for his jab at Reagan's tax proposals, Carter had little to say today about his GOP opponent. He told reporters that with Reagan's selection of George Bush as his running mate, the Republicans have "a good ticket" and that Reagan and Bush will be "formidable opponents."

Asked what he had thought of the possibility that Ford would be the GOP vice presidential nominee -- a prospect that surfaced for a few hours Wednesday night -- Carter said, "That would have been a pleasure either way."