The administration's dispute with House Speaker Jim Wright (D-Tex.) over Central American diplomacy boiled over at a White House meeting yesterday where President Reagan objected to Wright's activities and the speaker heatedly replied that he will keep "an open door" to both sides in the Nicaraguan conflict.

Wright demanded the meeting with Reagan, Secretary of State George P. Shultz, Vice President Bush, White House chief of staff Howard H. Baker Jr. and outgoing national security adviser Frank C. Carlucci. He acted after becoming infuriated by reports of administration anger at his efforts here last week with Nicaraguan President Daniel Ortega and Cardinal Miguel Obando y Bravo to promote peace talks between the Sandinista government and U.S.-backed rebels.

Following the meeting, Wright unleashed a barrage of alternately bitter and ironic comments in several sessions with reporters outside the White House and on Capitol Hill. He insisted that he had not forced himself into the talks last week, but had acceded to requests for help because he believes that Obando is the only person capable of mediating successfully between the contesting Nicaraguan factions.

"I'm not trying to replace Secretary Shultz," Wright declared. "I'm happy to be speaker." But asserting he did not need Shultz's permission to talk with "friends from other countries," Wright charged that some administration officials "are literally terrorized that peace might break out" in Central America.

He said regional leaders apparently prefer dealing with him because they have "the unfortunate impression that the administration treats them as inferiors, by scorning them, lecturing them, holding them up to public ridicule, and refusing to see them."

Responding to Wright's accusations, White House spokesman Marlin Fitzwater made clear how far apart Reagan and Wright have moved since August, when they collaborated on a Central American peace plan. Fitzwater said of the 40-minute White House meeting:

"The president expressed his concern over the speaker's role in getting involved in what should be essentially a matter between the Sandinista government and the Nicaraguan resistance with respect to negotiating a cease-fire. The president pointed out to the speaker the confusion that arises and the misleading impressions that can be left if members of Congress, without coordination with the executive branch, involve themselves in complex negotiations with foreign heads of government."

Shultz was described by administration sources as the official most upset by Wright's actions. The sources said the two had clashed in the meeting about whether the speaker had kept information from the secretary last week. State Department spokesman Charles E. Redman denied Wright's assertion that Shultz offered no objection when told last week that Wright would meet with Ortega.

Redman said that in a meeting with Shultz last Thursday, the speaker did not tell Shultz that he planned to meet Ortega and Obando the following day. Redman added that Wright phoned Shultz later Thursday to discuss the meeting, but "the secretary made it clear that he thought it was a bad idea."

Redman also confirmed that Shultz told Wright that if the meeting took place, the secretary would not meet with Obando out of concern that it would be interpreted as approval of a process the administration does not support. Asked if the administration had attempted to dissuade the Vatican's representative here, Archbishop Pio Laghi, from hosting the Friday meeting, Redman replied that the administration's views about how to conduct the peace process had been "described to all who cared to ask," including the archbishop.

Wright told reporters he hoped that the session had cleared up "misunderstandings and misapprehensions" about his activities. But he added: "I would not want to mislead you that they {the administration} feel I did the right thing. They don't. But I do not want to leave the impression that I am ashamed of anything I did. I'm not."

Wright said he still believes that Reagan and Shultz want a negotiated settlement of Central American conflicts.

But last week's events left no doubt that little if any common ground remained from attempts last August to forge a bipartisan approach to the Nicaraguan civil war and other regional tensions.

The Wright-Reagan initiative was a factor in prompting the five-nation peace accord signed Aug. 7 in Guatemala. Wright became a strong supporter of that plan. But the administration had second thoughts after key policymakers and conservative Republicans concluded that the Guatemala agreement lacked means to force the Sandinistas to cut ties with Cuba and the Soviet Union and that it would lead to abandonment of the contras.

In ensuing weeks, the differences hardened, such as when Wright pushed the administration to postpone until next year its planned request for $270 million in new contra military aid. But the rupture did not become public until last week when Ortega, here to address the Organization of American States, was encouraged by Wright to try to enlist Obando as go-between in indirect talks with the contras.

Wright's involvement, which attracted considerable news media attention, infuriated the administration. During the weekend, a senior official, who spoke on condition he not be identified, told The Washington Post that Wright's activities amounted to "guerrilla theater" and were "screwing up" the peace process. It was the Post article, Wright said yesterday, that prompted him to call the White House from Texas on Sunday and insist on a meeting.

In the meeting and in his public remarks afterward, Wright charged that the source for the Post article was Elliott Abrams, assistant secretary of state for inter-American affairs. Abrams has been controversial on Capitol Hill because of his tough anti-Sandinista position and his admission that he misled Congress about administration efforts to solicit funds for contra aid from other countries.

Wright added that the administration participants "did not admit and did not deny" Abrams' involvement. An aide said Abrams would not respond and the State Department told all of its officials not to discuss the matter publicly.

Rep. David E. Bonior (D-Mich.), chief deputy Democratic whip, said the administration had launched an unwarranted attack on Wright and complained about "someone like Elliott Abrams who comes to Congress and lies to us, taking cheap little snippy shots at us."