White House spokesman Marlin Fitzwater said yesterday that independent counsel Whitney North Seymour Jr.'s charge that the Reagan administration is insensitive to ethical issues was "an insult to the people of Washington."

Seymour, who successfully prosecuted former White House aide Michael K. Deaver, yesterday repeated the allegation he made Thursday against the administration, saying on CBS' "This Morning" that he was troubled by President Reagan's expression of sympathy for Deaver after his conviction.

Seymour said the president should have used the occasion to admonish his staff that he did not support any improper actions, such as lying to Congress or a grand jury, by government officials. "He {Reagan} let the country down," Seymour said.

But Fitzwater charged that Seymour's comments were improper and degrading to "government civil servants as well as political leaders thoughout the country.

" . . . I find it outrageous that he {Seymour} would find it wrong for one friend to feel sorry for the hardships of another, and he is totally out of line," Fitzwater said at his White House briefing.

The presidental spokesman also suggested that Seymour, who had delivered his attack Thursday on the steps of the U.S. Courthouse, may have not realized he was out of the courtroom. "You know any prosecutor worth his salt always goes before the jury and tries to posture himself in the most sanctimonious and self-righteous manner possible, and it appears that Mr. Seymour forgot where he was temporarily," Fitzwater said.

Charles E. Redman, a spokesman for Secretary of State George P. Shultz, responded yesterday to another Seymour charge -- that Shultz had been "irresponsible" in testifying on Deaver's behalf at his trial and had never read the charges against him.

"To try to argue that the secretary did not know what he was testifying is simply wrong," Redman said.

Deaver, 49, a longtime confidant and aide to the president, was convicted Wednesday on three counts of perjury for lying to a congressional subcommittee and a federal grand jury about his contacts as a lobbyist with high Reagan administration officials. He faces a possible sentence of 15 years in prison and a fine of up to $22,000 when he is sentenced Feb. 25.

Seymour, who maintained an extremely low profile during his investigation and the seven-week trial, began making public statements shortly after the verdict, noting that the law under which he was appointed calls for him to make reports to Congress and the public.

Yesterday, Seymour's office released a list of eight suggested changes to the Ethics in Government Act, which he told Congress illustrate shortcomings he discovered during the Deaver inquiry. Perhaps most controversial was his suggestion that a former government employe who works as an agent for a foreign country must first obtain a waiver of diplomatic immunity from that country about his activities.

That was an outgrowth of Seymour's celebrated effort to subpoena Allan E. Gotlieb, the Canadian ambassador to the United States, to testify about Deaver's work on behalf of the Canadian government. Gotlieb refused to waive his immunity and Seymour charged that was the reason Deaver was acquitted on one count of perjury.

The prosecutor also suggested that Congress overturn a ruling by the Office of Government Ethics that divides the White House into nine separate compartments, a decision that let former employes such as Deaver lobby workers in the eight other sections.