When The New York Times published a four-part series two weeks ago on alleged improprieties in the city medical examiner's office, the scrappy New York Post also picked up the cudgel.

In an assault reminiscent of the bare-knuckled battles that were common before the rise of the one-newspaper town, the Post, following true tabloid tradition of the best defense being a good offense, ran a two-inch banner headline last Friday that read: WHAT THE TIMES DIDN'T PRINT.

Under the headline, the Post revealed that one source quoted extensively in The Times, Dr. John Grauerholz, is the personal physician of right-wing political activist Lyndon Larouche.

According to the Post, Grauerholz testified in federal court in Virginia last October during a libel suit against NBC that Democratic presidential candidate Walter F. Mondale and The New York Times were members of an international narcotics lobby. He also said he believed that Mondale was a KGB agent.

The Post also reported that another Times source, Dr. Robert Wolf, had been convicted of income tax evasion and imprisoned.

Several other sources quoted in the series, the Post contended, were known adversaries of New York city medical examiner Elliot M. Gross.

"All this is bound to be embarrassing for The Times . . . ," New York Post executive editor Roger Wood said in a telephone interview.

"The Times is a very self-satisfied paper, and it's good that we should look after each other's interest by keeping an eye on what each other is doing," Wood added. "It certainly was not done in a sense of riposte. We were not counterattacking."

The Times, the city's stately newspaper of record, has maintained a dignified silence about the reports in the Post, which is published by newspaper magnate Rupert Murdoch. The Times series, written by reporter Philip Shenon, contains charges that Gross issued several false or misleading autopsy reports, some involving cases in which blacks and Hispanics died in police custody.

Mayor Edward I. Koch, Gov. Mario M. Cuomo and U.S. Attorney Rudolph Giuliani have launched five investigations into the medical examiner's activities.

Gross has taken a leave of absence to prepare responses to the allegations. He is also considering filing suit against The Times, said Howard Squadron, one of his attorneys, who also represents the Post -- a fact the tabloid has acknowledged.

On Feb. 3, following the advice of public relations executive Howard Rubenstein -- who also represents the Post -- Gross and his attorneys held a news conference to rebut The Times' charges.

The next day, The Times published Gross' statement in full, printed summaries of the examiner's rebuttal on specific points and ran a story on the conference. "We felt that was probably the most detailed response that could be given," said Leonard Harris, a Times spokesman.

Harris refused to answer questions about the Post's charges concerning Grauerholz's credibility.

The journalistic brawl is not over. Thursday's Post published a story saying that Dr. Michael Baden, a source quoted extensively in The Times' series, had a close relationship with senior Times editors, including executive editor A.M. (Abe) Rosenthal. "To Abe's knowledge, they have never met," Harris said.

In a story Friday, the Daily News -- the Post's major competitor -- questioned whether the Post's favorable coverage of Gross' side of the story might present a conflict of interest, because the tabloid and Gross are represented by the same attorney and by Rubenstein.

"I don't expect The Times will believe me," said Post editor Wood. "But I did not know that Howard Squadron represented Dr. Gross and I did not know, and there would be no reason for me to know, that Squadron would walk across the street and ask Howard Rubenstein for help."