Environmental Protection Agency Administrator Anne M. Burford made an emotional appeal to a group of conservative Republican activists 10 days ago to urge President Reagan to keep her on the job, GOP sources said yesterday.

Burford made the appeal to the Western States Political Caucus, a group of party officials and organizers from western states who worked for Reagan's election in 1980. One source who attended the Feb. 26 closed-door meeting in Denver said Burford was visibly shaken as she sought support.

It could not be learned whether her appeal had any direct result. But a week later Reagan told aides that he was unwilling to fire Burford and said she can keep her job as long as she wants to. Senior Reagan aides have been seeking Burford's removal because they say they believe she has become a serious political liability.

Burford received public support this week from Interior Secretary James G. Watt, who said in a speech in San Antonio that she is "taking abuse that no public servant should have to endure." But Sen. Alfonse M. D'Amato (R-N.Y.) yesterday joined other congressional Republicans calling for Burford's resignation.

Meanwhile, congressional Democrats investigating the EPA have been told that some documents they are seeking may have been destroyed or removed from agency files, and that a senior EPA official may have ordered erasures of items on his appointment calendars after they were requested.

Attempts to contact Burford about the Denver meeting through an EPA spokesman were unsuccessful yesterday.

Even as Burford was appealing to the Republicans to send a message to Reagan, the outlines of a Justice Department decision that jolted her the following week were taking shape.

Burford was cited for contempt of Congress last December, after she refused, at Reagan's order, to provide a House subcommittee with documents on the EPA's $1.6 billion Superfund to clean up toxic wastes. This claim of executive privilege was undertaken in part at the urging of the Justice Department, which unsuccessfully filed suit on Burford's behalf seeking to block the contempt citation.

Later, after allegations were made of mismanagement, conflict of interest and political manipulation of EPA programs, Reagan directed the Justice Department to investigate all charges of wrongdoing at the agency.

This confronted Justice Department lawyers with a potential conflict of interest because they would have to both investigate and defend Burford. How it was resolved more than two weeks later left Burford questioning whether the department and the White House had abandoned her.

Tom DeCair, chief spokesman for Attorney General William French Smith, said that immediately after Reagan's statement Justice Department attorneys began discussing how to resolve the apparent conflict.

The pressure on the department mounted Feb. 24, when Rep. Peter W. Rodino Jr. (D-N.J.), chairman of the House Judiciary Committee, sent Smith a letter asking questions about the apparent conflict and requesting internal documents about legal advice given Burford.

The White House was also aware, officials said, that the Justice Department was under some pressure to resolve the problem. White House counsel Fred F. Fielding talked with Deputy Attorney General Edward C. Schmults, said administration officials who added that Schmults was not acting on direct orders from the White House.

According to DeCair, the Rodino letter didn't affect the department's deliberations either. But he said Justice intends to reply to him by Rodino's Thursday deadline.

DeCair said a large factor pushing the department to reach some decision last week was another deadline--Burford's scheduled appointment to appear at House subcommittee hearings this week.

At a meeting last Thursday that administration officials have described as "stormy," Schmults and Assistant Attorney General Carol Dinkins, head of the Lands Division, informed Burford they could no longer represent her before congressional investigating panels. It remains unclear precisely what was said to Burford in this meeting. Schmults did not return calls this week and Dinkins said she would not comment.

But Burford and her aides came away with the impression that they had been deserted on the executive privilege claim she made at the request of Reagan and the Justice Department. Burford let it be known through aides that she understood Justice was dropping its defense of her in the executive privilege and contempt citation matters too.

In comments that irked some White House officials here and traveling with Reagan in San Francisco, Burford suggested that since the department was no longer representing her, she might release all the disputed EPA documents to Congress without restrictions the White House had previously demanded.

Administration officials said Fielding was informed of the Schmults meeting with Burford after it occurred.

The next day, March 4, Schmults sent Burford a letter outlining the department's position, but the paragraph on executive privilege was murky. After a weekend of confusion that was in part caused by the fact that White House officials were traveling with Reagan in California, the Justice Department issued another "clarifying" letter this Monday.

Clay Jones, an EPA spokesman, said yesterday that Justice "will defend us on any court action stemming from the executive privilege claim, anything before a real live judge. What they won't do is represent her and the agency in front of the committees in Congress."