President Reagan said Saturday Attorney General Edwin Meese's "name has been cleared" by an independent counsel investigation, but a Democratic spokesman said Meese "failed the American people."

Rep. Charles Rangel of New York, in the regular Democratic response to Reagan's weekly radio message, urged appointment of "someone that can restore the dignity and integrity to this great office" and lead the fight against illegal drugs.Meese announced Tuesday that he would resign next month, saying he had been vindicated by the investigation of his affairs by independent counsel James B. McKay. McKay's report has been filed in court, but not made public.

The White House has said the president hopes to nominate a successor to Meese during the coming week.

Reagan, speaking from the Oval Office, said, "With the announcement by Ed Meese, now that his name has been cleared, that he will be returning to private life this summer, I would like to take a minute to recognize a public servant of dedication and integrity who has been a close friend for over 20 years.

"As counselor at the White House and as attorney general, Ed Meese worked for stricter sentencing to put dangerous criminals behind bars and also for greater resources for drug enforcement and to fight organized crime," Reagan said.

He said Meese also "led our Justice Department as it aggressively defended civil rights" and "achieved more convictions for civil rights violations than any previous administration."

The president lauded Meese's anti-terrorism efforts, saying he "worked closely with our allies to detect, apprehend and prosecute those who wage war on innocent members of free societies."

Rangel said Meese had failed Reagan both as a friend and as the member of his Cabinet who should have led a broad-based anti-drug effort.

"Mr. President, now that the attorney general has finally resigned, I sincerely hope that you will take the initiative to appoint someone that can restore the dignity and the integrity to this great office that it deserves," Rangle said.

Rangel, who is chairman of a special House committee on drugs, said one of Meese's failures was "not putting together the type of Cabinet team necessary to start the fight in the war on drugs."

After enumerating what he said were other shortcomings of Meese, Rangel said, "Loyalty is one thing, but when you list those failures of this personal friend, the attorney general, you cannot overlook how he has failed to bring together this team to be engaged in the war on drugs."

Reagan also spoke about the drug issues in his speech, announcing that White House employes were told on Friday that random drug testing will begin in 60 days.

He also renewed his appeal to Democratic leaders in Congress to appoint members to an executive-legislative drug task force.