The congressional investigation of Thomas C. Reed's appointment to a sensitive National Security Council post has set off a chain reaction of blame-fixing that has entangled two subcommittee chairmen, the Securities and Exchange Commission and, potentially, the president's national security affairs adviser, William P. Clark.

The situation began when the staff director of a House oversight subcommittee said that the SEC "took a dive" in its investigation of Reed's stock trading.

An indignant SEC chairman then asked that the staff director meet with the SEC to explain his remarks. But the staff director's boss, the Democratic chairman of the subcommittee, refused.

So, the SEC chairman sought a friendlier forum: in the Senate, where the oversight subcommittee chairman is a Republican, who agreed to let SEC officials have their say in a hearing.

Now, some Senate Democrats have urged the Republican chairman to broaden the hearings to include "the role of the White House."

The hearing begins at 1 p.m. today.

Reed announced last week that he will leave the NSC in April after the completion of his assignment to President Reagan's commission on a basing strategy for the MX missile.

The announcement followed the disclosure that a federal grand jury in New York is investigating whether Reed violated criminal statutes in March, 1981, when he turned a $3,125 investment in stock options into a $427,000 gain.

On the day of the announcement, last Tuesday, SEC Chairman John S.R. Shad wrote to Rep. John D. Dingell (D-Mich.), chairman of the House subcommittee that oversees the securities agency, with a strong complaint.

"Your staff director . . . was quoted in The Washington Post and on . . . CBS' '60 Minutes' to have stated that the SEC and its staff 'took a dive' in the Thomas Reed case."

The case Shad was referring to was a December, 1981, civil settlement between Reed and the SEC disposing of civil charges that Reed had traded on "insider" information in the same stock transaction. Under the settlement, Reed agreed to put the $427,000 aside to pay off investors who could prove that they were hurt by his stock trading.

After a review of the SEC's investigative files in the case, Dingell's staff director, Michael F. Barrett Jr., told The Washington Post that the files showed that the SEC "took a dive" in the case.

Barrett's remark was repeated the following day by Mike Wallace on a "60 Minutes" segment about the Reed case.

"This is a grave charge made before an audience of over 50 million," said Shad in his letter. Shad requested that Dingell send his staff director to meet with the commissioners last Thursday "to explain his charge."

Ignoring the request, Dingell wrote the SEC chairman the following day saying, "The commission will have an opportunity to discuss its views on its handling of the Reed case when it apppears before the subcommittee as part of our oversight review of the commission's enforcement program."

Dingell said that his staff had found "a number of problems which we believe the commission should have considered during its disposition of the case."

Among them:

* The SEC settlement "suggests that the action was dropped because it didn't have merit and creates a misleading impression," according to a subcommittee memo prepared by Irwin Borowski, a former senior SEC attorney.

In defending its hiring of Reed, "The White House . . . relies heavily on the fact that the complaint was dismissed . . . ," Borowski said.

* "The commission did not, as is usually the case, obtain a separate injunctive decree . . . directing Reed not to engage in" insider trading in the future, but rather entered into a milder "stipulation," Borowski's memo said.

"This allowed Reed to minimize the action taken against him and claim no court decree was entered . . . , " the memo said.

* Reed was allowed to state that he cooperated in the commission's investigation.

"As evidenced by the action the commission took against him . . . it was the commission's view that Reed had lied throughout his testimony in denying he had received inside information . . . , " the Borowski memo said.

The next development occurred late last week when Sen. Alphonse M. D'Amato (R-N.Y.) announced that his oversight subcommittee would hold hearings today featuring Shad as a leadoff witness to determine who did or didn't "take a dive" in the Reed case.

On Sunday, four Democratic senators, William Proxmire (Wis.), Paul S. Sarbanes (Md.), Donald W. Riegle (Mich.) and Christopher J. Dodd (Conn.), wrote to D'Amato asking him to call Clark and his chief of security, Richard C. Morris, to explain how the SEC investigation was weighed by the White House.

"It is our understanding that Mr. Reed's securities trading activity was well known to the White House before his appointment . . . and we would like to investigate in full detail how and why this appointment was made . . . . "

Dingell aides, who met last week with Morris, said Clark was told in June, 1982, by Morris that Reed's past stock trading activities would be an ongoing political problem and a source of potential embarrassment to the administration.