The Virginia Republican Party restarted its campaign for the U.S. Senate here yesterday with a new candidate and a promise by Gov. John N. Dalton to "send the message all over this state" that the Carter administration is soft on communism.

Shouting his support for GOP senator nominee John W. Warner, to a crowd of party picnickers, the governor read aloud a Richmond newspaper editorial entitled "Soft" critical of administration defense budget cuts.

"Don't blame the Republicans," the Richmond News Leader editorial said, "if they start politicking on the contention that the current president is soft in defense and not illogical corollary that he is soft on Reds."

"We're going to send that message all over this commonwealth in the weeks to come," using the Warner campaign, Dalton said.

Warner himself, secretary of the Navy under President Richard Nixon, promised the crowd he would "flush those doves out of the Pentagon" if elected and promised to "rebuild the momentum we had under President Ford for our United States Navy."

Warner spoke just a short distance west of the mammoth Newport News Shipbuilding and Dry Dock Company, economic mainstay of the Virginia Peninsula and one of the largest shipyards in the world. And he drew cheers by accusing the Carter administration of playing politics with the carrier Saratoga by attempting to shift the site of its overhaul from Newport News to Philadelphia.

"That's the kind of politics you will never catch me involved in," Warner said. Democrat Andrew P. Miller, Warner's opponent, predicted Friday in Norfolk that the Navy will reverse its decision and ovrhaul the carrier here, saving $80 million.

Warner also addressed a press conference shortly before the picnic at which he was asked about comments made earlier in the week by his former chief of naval operations, retired admiral Elmo Zumwalt.

Zumwalt, who ran against Virginia's independent Sen. Harry F. Byrd Jr. two years ago, described Warner as a "dilettante . . . who doesn't do his homework," and as a man who owed his senate nomination to the fame of his current wife, actress Elizabeth Taylor, and the money of his first wife, heiress Catherine Mellon.

Zumwalt said Warner's opponent, Democrat Andrew Miller, would make a much better senator than Warner, but that the late Richard D. Obenshain - whom Warner was nominated Aug. 12 to succeed - would have made a better senator than either.

Warner described Zumwalt's remarks as an effort by Miller to "call in reinforcements" and added: "He (Zumwalt) took a pass at my wife, which interested me. You know I talked the other night with my first wife, who is solidly behind me in this campaign.

"If you look around in the crowd, my second one's here somewhere. So with that I simply say to Adm. Zumwalt perhaps he should go back and study the Bible. I think it's Exodus, Chapter 20, Verse 17: 'Thou shalt not covet another man's wife.'"