President Reagan tried yesterday to calm congressional fears that he is inflexible on budget issues, saying that talks aimed at producing a bipartisan compromise were reaching a "climactic stage" and that it was his "strong hope" they would succeed.

"He's trying to convey to our Republican friends on Capitol Hill that he's not intransigent," a senior White House official said later in the day.

Some Republican senators have become restive about Reagan's lack of involvement in the negotiations, which are to resume Sunday with another session scheduled for Tuesday. Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) has said that he will ask the Senate Budget Committee to begin writing its own budget resolution next week if the negotiations do not succeed.

"We've tried to approach the undertaking in a constructive and conciliatory spirit," Reagan said in a speech to southeastern broadcasters gathered in the state dining room of the White House. "We'll continue to do so in the days ahead."

Reagan then went on to give his standard speech opposing any change in the 10 percent tax rate reduction that will become effective July 1 and the additional 10 percent cut scheduled for July 1, 1983.

"Tampering with the third year of the tax cut or saying, 'All right, we will keep that third year but then we will increase taxes again in the fourth year and every year after that,' would inflict major damage on the economy," Reagan contended.

White House officials said that the president's statement was phrased so as not to rule out a proposed 4 percent income tax surcharge that is expected to be a part of any agreement produced by the negotiators.

The administration view expressed by two aides yesterday was that the surcharge would be acceptable if it was part of a package containing limitations on cost-of-living increases for Social Security recipients.

Because neither Reagan nor House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) want to be associated with any possible reduction of Social Security benefits, they have not been part of the direct negotiations.

Reagan said earlier in the week that he would "stay on the sidelines" in the budget talks, which he then insisted were only "discussions," not "negotiations."

White House deputy press secretary Larry Speakes, responding to a question about whether Reagan had become more interested or involved in the talks, said: "He's on the sidelines, but he's probably perked up a little bit."

One reason for the president's lack of direct involvement in the discussions is that he faces a potential revolt in Republican ranks if he accepts a surcharge in order to win Democratic support. Yesterday, Sen. William V. Roth Jr. (R-Del.) circulated a letter signed by seven other Republican senators calling on Reagan to reject any surcharge proposal.

Going into what appears to be the decisive stage of the negotiations, White House officials declined to make a prediction on the budget talks except to say that they were entering a crucial stage.

On Wednesday, a White House official estimated the chances of success as no better than 50-50 and said that the strategy of compromise would be followed by one of confrontation if the negotiations break down.

At the White House briefing yesterday Speakes was asked about Reagan's statement in Chicago on Thursday to an eighth-grade school class. Reagan told the pupils that in Britain, prior to the abolition of capital punishment, any criminal caught with a gun in his possession was automatically tried for first degree murder and was hanged if he was convicted.

"It's just not true," a reporter said at the briefing.

"Well, it's a good story, though," Speakes responded with a smile. "It made the point, didn't it?"