Democratic presidential candidates have begun targeting Edwin Meese III, apparently believing that the troubles of the attorney general provide a fertile and popular ground for public criticism.

Sen. Paul Simon (D-Ill.), a candidate for his party's nomination, launched a strong assault on Meese yesterday, calling for his resignation in a weekly Democratic radio broadcast.

"Ed Meese would do the president and the nation a service by resigning," said Simon in the Democratic response to President Reagan's weekly radio broadcast.

A spokesman for Meese called Simon's statement an attempt to get "a cheap headline two days before the Iowa caucuses." The spokesman said Meese "hasn't done anything wrong."

Simon is the latest Democratic presidential hopeful to attack Meese in recent weeks. On Jan. 19, former Arizona governor Bruce Babbitt called for Meese to quit or be fired. Meese has been a regular target of the Democratic presidential candidates for months.

"We need an attorney general who will spend his time in court as plaintiff, not a defendant," Jesse L. Jackson said in a formulation all of the other Democratic candidates have used as well.

Democrats are hoping that what Rep. Richard A. Gephardt (D-Mo.), another presidential candidate, regularly calls the "sleaze factor" will become a major campaign issue against the Republican nominee in the general election. Gephardt oftens runs down a list of high Reagan administration officials who have left office under a cloud of accusations.

Simon, referring in yesterday's broadcast to investigations of Meese's actions in a proposed Iraqi pipeline deal and in the defense contract operations of the Wedtech Corp., said, "I do not presume that any of the reports are true." But he said that an attorney general should be an individual of "stature and eminence to whom all Americans can look with pride."

He said respect for the law is diminished by questions surrounding Meese's conduct, by "insensitivity to civil rights and civil liberties," by the fact that the Justice Department "does almost nothing to enforce the nation's antitrust laws" and that "the person who heads our Department of Justice is generally regarded as having been selected for his friendship to the president rather than his dedication to justice."

"This is a cheap headline two days before the Iowa caucuses. It's hardly original," said Patrick S. Korten, deputy director of public affairs at the Justice Department. "There is absolutely no reason for him {Meese} to resign. He hasn't done anything wrong. I think it would be very nice if Paul Simon would presume innocence just as the legal system does. Whatever else he may be saying about his presumptions, it boils down to a presumption of guilt."

Staff writer Paul Taylor contributed to this report from Des Moines.