WASHINGTON, Dec. 18— Archibald Cox, the chairman of Common Cause, today attacked Edwin Meese 3d, saying the Presidential counselor had displayed a ''lack of ethical sensitivity'' and ''blindness to abuse of position,'' and he urged Senators to vote against confirming Mr. Meese to the post of Attorney General.

Mr. Cox, the first Watergate Special Prosecutor and now head of the public affairs lobby, said in a letter sent to all Senators today that a court-appointed independent counsel's investigation into charges of wrongdoing by Mr. Meese had not, in fact, vindicated him, as the Administration has insisted.

Rather, Mr. Cox said the report issued three months ago by the independent counsel, Jacob A. Stein, showed that Mr. Meese lacked the judgment and ethical standards required of an Attorney General.

The independent counsel's investigation focused on allegations that Mr. Meese had helped arrange positions in the Reagan Administration for individuals who had assisted him financially and that he had failed to disclose, as required by law, a $15,000 interest-free loan to his wife.

A 37-page review of Mr. Stein's report, prepared by Common Cause, noted that Mr. Stein had found no basis for prosecuting Mr. Meese for any violation of Federal criminal law. But the review pointed out that Mr. Stein had refused requests to evaluate Mr. Meese's fitness to become Attorney General as a question beyond his jurisdiction.

Mr. Cox's letter said it was the first time that Common Cause, which calls itself a citizens' lobbying group with 250,000 members, had opposed confirmation of a Cabinet-level nomination.

Leonard Garment, Mr. Meese's lawyer, when reached for comment, said: ''Common Cause misreads the significance of the report and takes material out of context in order to make an overall negative point. We reserve further comment for the confirmation proceedings.''

The hearings are expected to be reopened by the Senate Judiciary Committee in late January or early February. In spring, the committee postponed action on Mr. Meese's nomination to replace Attorney General William French Smith after the Justice Department opened a preliminary inquiry into charges of wrongdoing by Mr. Meese. The department then relinquished the inquiry by asking a special three-judge panel to appoint an independent counsel under provisions of the Ethics in Government Act.

The Common Cause review of the independent counsel's report stressed, however, that it should not be viewed as an affirmation of Mr. Meese's qualifications to occupy the post of the nation's top law-enforcement officer.

The White House spokesman, Larry Speakes, said today that President Reagan had ''no reaction'' to the views expressed by Common Cause.

Senator Howard M. Metzenbaum, Democrat of Ohio, who led the attack on Mr. Meese at the first round of confirmation hearings on his nomination, said he agreed with Common Cause and intended to make some of the same points when the hearings start again. Transition Trust Question

Mr. Metzenbaum said these would include questions about Mr. Meese's Army Reserve promotion and questions about a payment Mr. Meese received from a trust set up to help finance Mr. Reagan's 1981 transition to the Presidency.

The Common Cause report says Mr. Meese received $10,000 from the Transition Trust, which was designated as ''moving expenses'' and deposited in his bank account.

But after learning that the Justice Department would probably consider payment of moving expenses a violation of criminal law, the review says, Mr. Meese directed that trust records be changed ''to reflect that his check was for 'consulting fees,' which he reported as income on his tax return.''

Mr. Metzenbaum said he intended to vote against Mr. Meese's confirmation.