Virginia State Sen. Nathan H. Miller, the Republican nominee for lieutenant governor, acknowledged today that he had "an apparent conflict of interest" in drafting and voting for legislation giving his law clients, the state's electrical cooperatives, $13.2 million in tax breaks and business advantages.

Miller also said he should have disclosed to his Senate colleagues that he had written the bills for the co-ops, which paid him at least $250,000 in legal fees during the last seven years. At least a dozen of those bills were introduced and sponsored by other legislators who were sometimes unaware of Miller's authorship.

"Hindsight is 20-20 and I wouldn't go through this again," Miller said at a press conference at the State Capitol.

But Miller insisted he had violated no law and said he would not hesitate to vote as a senator or lieutenant governor for a co-op measure he had authored, provided the bill was in the best interests of the state.

"The bottom line in these matters is a matter of what's right and wrong...I didn't think I did anything wrong," he said.

The Rockingham County Republican called the news conference to rebut growing criticism over his dual role as state senator and utility lawyer, details of which were first revealed in a Washington Post story a week ago. Critical editorials in Richmond, Roanoke and Norfolk newspapers, which in recent years have backed Republican candidates, have added to the controversy over Miller's actions.

When first questioned by the Post about his activities, Miller denied there was any conflict and rejected a request to make his income tax returns public. When the story appeared, Miller did not deny its contents but accused the newspaper of writing the article because of its "liberal bias."

Today, Miller took a different approach, allowing an "apparent conflict" but saying that every one of Virginia's 140 lawmakers suffered from similar conflicts because all are part-time legislators who have business interests. Miller also released his 1980 tax returns and a detailed financial statement.

The statement put the 38-year-old lawyer's net worth at $784,000. His income tax return for l980 revealed that, by using investment credits and other income adjustments, Miller paid federal taxes of $2,098 on an adjusted gross income of $18,984.

Miller's role did not come up during yesterday's General Assembly session here, but many legislators, including members of his own party, were privately critical of his relationship with the cooperatives. State Sen. Howard Anderson (D-Halifax), who introduced one of Miller's bills at the request of a co-op lobbyist, has complained publicly that Miller should have told him he had drafted the measure.

Miller said today many of his legislative critics had partisan motives and suffered from as many conflicts as he did. "The Democrats have controlled the General Assembly all the years I've been down here and I'm sure plenty of them have plenty of good clients around . . . . I haven't seen them stand up in righteous indignation until it's a Republican that's getting criticized."

Miller, who during the 1981 session voted against a bill to tighten the General Assembly's conflict-of-interest rules, today said he would support such legislation. He said the current written disclosure form required by the legislature, "doesn't really tell you anything."

At the press conference he again refused to reveal how much he had been paid in legal fees from the co-ops, citing an attorney-client relationship. But he did not dispute the $250,000 figure in the Post's account.