The Justice Department, seeking to smooth an acrimonious dispute with Environmental Protection Agency Administrator Anne M. Burford that spilled over into the White House, said yesterday that it would continue to represent her in President Reagan's claim of executive privilege over EPA documents sought by Congress.

But the department again refused to defend her before congressional panels investigating the EPA.

In a letter to Burford, Deputy Attorney General Edward C. Schmults said he wanted to "correct any misapprehensions" about the department's role as it simultaneously investigates the EPA and represents the agency. Schmults said separate sections of the Justice Department would continue to do both.

The letter came after a stormy weekend in which Burford had lashed out at the Justice Department and presidential aides, claiming that she had been abandoned by them. They responded by accusing her of disloyalty to the president.

Although some presidential assistants are known to want Burford's resignation, White House spokesman Larry Speakes yesterday described as "conclusive" and "definitive" the president's statement in Oregon Saturday that Burford could keep her job "as long as she wants."

Speakes said Reagan has not barred his staff from seeking Burford's resignation, although he suggested that they should "keep their toe out of that water." White House officials were under orders yesterday not to talk to reporters about the EPA controversy.

Also yesterday:

* Rep. Edward J. Markey (D-Mass.) urged House Energy and Commerce Committee Chairman John D. Dingell (D-Mich.) to seek prosecution for perjury of EPA general counsel Robert M. Perry. Markey said Perry had lied under oath about existence of "green books" kept by Perry's staff that contain critical remarks about some of his EPA subordinates. Perry said he "did not lie."

* At a hearing before Dingell's oversight subcommittee, Perry disclosed that Burford had suggested last week to Justice Department officials that they name a special prosecutor to handle the charges of wrongdoing at the EPA, but he said the idea was rejected.

The Justice Department letter to Burford yesterday was said by administration officials to be an effort to "clarify" further the extent to which the department would help Burford in the executive privilege case, which she undertook at Reagan's orders.

The EPA originally refused to turn over some documents on the $1.6 billion "Superfund" to clean up hazardous wastes. After Burford was cited for contempt of Congress, the administration agreed with one House subcommittee to an arrangement allowing examination of the documents.

Six congressional panels are looking into allegations of mismanagement, conflict of interest and political manipulation at the agency.

An informed White House official said Burford became angry last Thursday when told at a meeting with Justice officials that the department could not represent her on the executive privilege matter. The next day she received a letter from Schmults outlining the department's position.

The letter said Justice Department officials had not changed their position on executive privilege and would still defend the president. While the letter said they could not represent Burford before congressional investigating panels, it did not address representing her in other executive privilege matters.

Burford told aides that she felt the White House and Justice Department were abandoning her on a position they had insisted she take. White House officials, traveling with Reagan in San Francisco that day, also were angered by Burford's suggestion that she might make all of the disputed EPA documents available to Congress without restrictions previously set by the White House.

"It was overblown," one White House official said yesterday, adding that it now appears that the Justice Department has only backed away from representing Burford before the investigating panels. EPA spokesman Rusty Brashear said the latest Justice Department letter was interpreted yesterday as "a real backing off of their earlier position as we understood it last Thursday." Burford is scheduled to appear Thursday before Dingell's panel on the contempt citation, and Brashear said she would attend the hearing alone.

Schmults said in his letter yesterday that the Justice Department would not represent Burford "before congressional committees engaged in investigating the same allegations which are being looked into by the department."

But he said the department would still defend her in the "pending civil action" stemming from the executive privilege case--a lawsuit filed by the Justice Department to block the contempt-of-Congress citation against Burford. The case was dismissed by a federal district court judge.

Should the contempt case be pursued further by the House, Schmults said "we do not anticipate" that the department would abandon Burford, even though the department's Criminal Division is investigating the agency.

A White House official said last night that no meeting is scheduled between Burford and Reagan, but neither administration nor EPA sources would rule one out this week.

At yesterday's hearing before the Dingell subcommittee, Markey noted statements by EPA general counsel Perry, dating to last December, that he had no knowledge of a "green book" containing comments critical of his subordinates.

Markey said the subcommittee had heard testimony in closed session that Perry had been perturbed last August when a lawyer on his staff had failed to brief him on a court decision that affected EPA and in which the White House was interested. According to an unidentified witness cited by Markey, Perry "yelled" to his secretary to "get that green book" and take 50 points off the lawyer's rating.

Markey said the subcommittee also had testimony from other EPA employes describing the existence of "green books" that included a similar point system to keep track of employes' performance. "I had not directed anyone to maintain a green book, nor do I keep a green book," Perry insisted.

Markey then held up three of the books kept by Perry's aides. Perry later conceded that he might recognize those books or others like them.

"I was thinking of an entirely different type of green book," he said.

"I find your testimony appalling," Markey said. " . . . You insult the intelligence of everyone listening. I wish one lesson people could learn from Watergate is that the truth is the best defense."

"Sir, I did not lie. I would not have to lie . . . . I can only tell you that at the time I testified I was telling the truth, and I'm still telling the truth," Perry said.

In response to further questioning, Perry conceded that as a former attorney for Exxon Corp. he should have disqualified himself from involvement last year in the EPA's $2.3 million settlement for cleanup of the Chem-Dyne waste dump in Hamilton, Ohio, where an Exxon subsidiary was one of the polluters.