Acting Secretary of Transportation James H. Burnley testified yesterday that former White House aide Michael K. Deaver called him about a petition filed by one of his lobbying clients but made no effort to influence him.

In fact, Burnley said, he may have placed the call to Deaver after learning that he was attempting to reach Burnley's boss, then-Transportation Secretary Elizabeth Hanford Dole.

Burnley, a lawyer who told the jury he was familiar with the Ethics in Government Act, said he saw nothing improper with the brief conversation. Deaver "made no specific remarks as how we ought to handle" a pending request by Trans World Airlines, one of his clients, Burnley said.

"He made no attempt to tell me what his opinion was or to influence or to lobby," said Burnley, who was named by President Reagan to succeed Dole but has not yet been confirmed by the Senate.

Deaver, the Reagan administration's former deputy chief of staff, is accused of lying about whether he contacted "any government official" on behalf of TWA. The charge is part of a five-count indictment that alleges that Deaver, a longtime confidant of President and Mrs. Reagan, lied to a congressional subcommittee and a federal grand jury in an effort to cover up various contacts he made on behalf of the lobbying firm he established after leaving the White House in 1985.

Deaver is accused of discussing with Burnley TWA's effort to block a hostile corporate takeover. He is also alleged to have had the same discussion with Dole in a telephone call in the summer of 1985. Yesterday, the seventh day of testimony, prosecutors introduced what defense lawyers described as what "may be the only evidence" that the conversation with Dole occurred.

U.S. District Court Judge Thomas Penfield Jackson, rejecting arguments by Deaver's lawyers, allowed the prosecutors to introduce two pages of telephone logs from Dole's office that showed that Deaver made repeated efforts to reach her and that they apparently talked on one of the days.

Dole's personal secretary, Shirley Ballard, said she prepared the logs and believed them to be accurate, but she said that she could not verify that the conversations actually occurred or that Deaver was the person who had called the office seeking to talk to her boss.

"If the defense wants to suggest that some impostor made four calls to Elizabeth Dole's office saying he's Michael Deaver, then God bless them," said prosecutor Marc J. Gottridge in arguing that the telephone logs should be admitted.

Later with the jury present, Randall J. Turk, one of Deaver's lawyers, asked Burnley if Dole would remember the conversation, hinting that she would not recall it. Dole, who left the department last month to join the presidential campaign of her husband, Sen. Robert J. Dole (R-Kan.), is one of the more than 250 people who have been listed as possible witnesses at the trial.

If admission of her telephone logs was a setback for the defense, Burnley's statement that he saw nothing improper in Deaver's call was a plus. Former White House aides Roger Porter and Rear Adm. John M. Poindexter have testified that in telephone calls made to them, Deaver made no effort to pressure them.

Charles R. Black, a Washington political consultant who was also hired to work for TWA in an effort to block the takeover, testified yesterday that Deaver was specifically assigned the task of contacting Dole and that he knew of no other assignment that TWA officials gave Deaver.

Deaver's firm had a $250,000-a-year contract with the airline, and the prosecutor has alleged that he did little work for the six-figure fees he received.

Black said in response to questions from a Deaver lawyer that he viewed the size of the fees Deaver charged his international clients, from $100,000 to $475,000, as on "the low end of the range" charged by most Washington lobbying firms. He said his firm, Black, Manafort, Stone and Kelly, has one international client it charges $800,000 a year. He did not identify the client.