AUSTIN, Texas (AP) _ A lone Republican candidate hopes to break the Democratic grip on a U.S. House seat in a special race being held today despite objections that Gov. Mark White did not get federal approval of the election date.

Six Democratic candidates want their party to hold onto the seat representing this northeast Texas district vacated when Sam B. Hall Jr. became a federal judge. It formerly was held by Wright Patman and Sam Rayburn.

Voter turnout in some areas appeared moderate two hours after the polls opened at 7 a.m., officials said.

The race is viewed as a test of growing Republican strength in a traditionally conservative Democratic part of the state. A runoff would be needed if no candidate gets a majority of the votes.

Edd Hargett, the GOP contender, is running against state Reps. Sam Russell and Jim McWilliams, former state Treasurer Warren G. Harding, Carl Brown, Jim Chapman and Billy Flanagan. Fred Wieder is running as an independent.

In a Thursday letter to White, the U.S. Justice Department threatened legal action to block the election because the date was not ''precleared'' with the federal agency as required by the Voting Rights Act.

White, who set the election date on May 28, responded Friday with a letter saying his decision was not subject to federal review. Texas Democratic Party Chairman Bob Slagle responded with a statement charging the Reagan administration with ''meddling.''

Assistant U.S. Attorney General William Bradford Reynolds told White the one-month notice was too short, not allowing ''sufficient time, particularly for citizens overseas, to learn of the election and to take the actions necessary to cast a ballot.''

Reynolds also said federal officials were supposed to review the special election date to make sure it ''will not have the effect of discriminating on account of race, color or membership in a language minority group.''

''If the state elects not to comply voluntarily with the provisions (of the Voting Rights Act), it may be necessary to institute legal proceedings to obtain compliance,'' Reynolds told White.

The necessary federal review could have been completed in 24 hours, according to Reynolds.

White replied Friday, saying state lawyers determined there was no need to obtain federal preclearance.

Texas Secretary of State Myra McDaniel, the state's top election officer, said the voting would go on as scheduled.

''I am certain that this matter will be resolved and that the election will take place without difficulty,'' she said.