John W. Warner, the former Navy secretary who narrowly lost the Republican nomination to the U.S. Senate in Virginia on Saturday, said yesterday that he remains very much interested in running for elective office.

Interviewed by phone at his Fauquier County farm, Atokn, Warner said he does not know what office he might seek. Asked if he would consider running against independent U.S. Sen. Harry F. Byrd Jr. in 1982, he said:

"I think that it is from the impressive growth of the Republican Party that there will be a Republican candidate in every House and Senate race in the future in Virginia, but I wouldn't indicate now that I will be available for the seat."

Warner will be 54 in 1982. Virginia Republicans did not field an opponent against the conservative Byrd in 1976, when he easily defeated Democrat Elmo Zumwalt, but GOP leaders said then that Byrd is certain to have Republican opposition in the future if he himself does not switch to the GOP.

Conservative Republicans in Virginia have tried to lure Byrd into their party ever since he began running as an independent rather than a Democrat in 1970. They were hopeful after 1973 that he would follow his close friend, former governer Mills E. Godwin, into the GOP, but he did not. Although he ran as an independent in 1976, he still is a member of the Democratic caucus in the senate.

Warner's plans to remain active in elective politics have the full approval of his wife, actress Elizaberth Taylor, who helped propel him into the voters' consciousness with countless public appearances during the last two years.

Taylor came to the phone during the interview and declared: "We're not quitting. I don't know what office it will be, but I'm sure something will come up".

Taylor leaves this week for three weeks in California where she will appear in a "Hallmarks Hall of Fame" film for television.

Warner lives in the 7th Congressional District, which is represented by Republican J. Kenneth Robinson. Asked if he would consider running for that seat if Robinson retires in 1980, Warner said, "I would hope that Ken Robinson would stay in Congress. He's a good friend of mine and the kind of man we need more of in national office."

Warner said his immediate plan is to join a nonprofit defense research organization specializing in naval affairs and strategic arms limitation policy.

At the Republican state convention Saturday, Warner was closing fast on front-runner Richard D. Obenshain when dark horse candidate Nathan H. Miller withdrew after the fifth ballot and released enough delegates to give Obenshain a small majority on the sixth.

Looking back as his narrow loss, Warner said, "This is Monday morning quarterbacking, but I believe if Miller had stayed in we would have gradually picked up the votes to win. We had the momentum."

Warner said he believes that Godwins's endorsement of Obsenshain and lobbying by the former governor on the convention floor for the eventual nominee "was indeed an influence."

"I talked to Governor Godwin about four days before the convention," Warner said, "and he told me that he could support either myself or Obenshain. But he said he felt a special obligation to Dick because of his role in putting to coalition that supported him for governor in 1973."

Warner said he thought Miller would never withdraw because Miller had told him before the convention he intended to stay in the race until the end. "I came to know him as a Christian gentlemen during the campaign and I took him at his word," Warner said. He added, "I tell you though that I look back at it all with no bitterness toward anyone."

Godwin met with Miller during the fifth roll call and is thought by many Republican campaign officials to have persuaded Miller to get out of the race rather than incur the ill will of Obenshain supporters, who could help or hurt the young state senator in future bids for office.

Miller, however, said in an interview yesterday that Godwin merely asked him if he would release five votes in Godwin's 4th Congressional district delegation and did not pressure him to withdraw from the race.

"I got out after the fifth ballot because my vote total was going down, Miller said. "It looked like we would not succeed in our strategy of deadlocking the convention and winning as a compromise candidate, so I withdrew. I thought I had asked all I had could of my supporters".