With the resignation of Sen. Harrison A. Williams Jr. (D-N.J.) behind them, members of the Senate moved toward an investigation of what many say they believe is an even more important issue: whether the FBI overstepped its bounds and used illegal tactics in the Abscam operation that led to the conviction of seven members of Congress.

Sens. Alan Cranston (D-Calif.) and Ted Stevens (R-Alaska) introduced a resolution, believed to have broad support in the Senate, calling for a full investigation of the FBI and Justice Department's handling of Abscam and any other similar operation aimed at government employes.

During six days of debate the Senate heard charges from Williams and other members that Abscam was a series of crimes dreamed up and encouraged by the FBI in an attempt to entrap innocent members of Congress.

In looking back over the debate, Williams said yesterday, "I sought not only my own personal vindication, but also the reaffirmation of a fundamental principle of our nation: that individual citizens, whether they be laborers, businessmen or, yes, United States senators, shall not be given 'criminality tests' by law enforcement officials."

While Williams was not able to convince most members that he was an innocent victim of overzealous law enforcement officers, the serious questions about FBI conduct remained.

Sen. John C. Stennis (D-Miss.) accused the FBI of being a "national disgrace." He said, "I'm convinced that we just have to put a total prohibition on these people charged with law enforcement that they shall not get out of their field. They just can't instigate the violation and then turn around and try it. It won't work."

Stennis said he will ask for a law to require court approval for Abscam-type operations. Congress should "lay down a law that must be obeyed by the FBI," he said.

Sen. David H. Pryor (D-Ark.) agreed. "I think now is the time to establish some checks and balances, to establish parameters in which the FBI can operate. I hope the message does not go out that we think we're immune from investigation, above the law. We're not. But the FBI has shown a total, callous disregard for the rights of citizens."

Senators were particularly angered by a memo introduced Wednesday by Pryor indicating that FBI Director William H. Webster personally had approved the offer of an Abscam bribe to Sen. Larry Pressler (R-S.D.). Pressler did not take any money and was never accused of wrongdoing.

The Nov. 7, 1979, memo, initialed by Webster, indicated that the bribe had been authorized for Rep. William J. Hughes (D-N.J.), but that Pressler was brought in as a substitute when Hughes couldn't come to the meeting.

The FBI, which refused yesterday to comment on the memo, had countered charges of entrapment by insisting that the Abscam middlemen had been instructed to bring in only members of Congress who were prepared to take part in a criminal act.

"It was always told or implied to us by the FBI that some middle-echelon official had authorized the action against Mr. Pressler. The Ethics Committee was assured some middleman had made this authorization, and the FBI was apologetic about it," Pryor said.

Late yesterday Webster moved to defuse this part of the issue. Pressler said Webster came to his office with a letter of apology saying that Webster had "no reason to believe you were engaged or would like to engage in a crime."

Earlier, Sen. Patrick J. Leahy (D-Vt.) said, "They decided, 'Well, we've got the apartment rented for this afternoon. Let's not let it go to waste. Let's see what member of Congress comes across the street so we can grab him.' That's just not good law enforcement."