The Senate has given President Carter an invitation to veto a $10.8 billion energy and water resources spending bill and Interior Secretary Cecil D. Andrus is uring him to accept it.

Andrus sent word to the White House yesterday that he thinks a veto is mandatory as a result of Senate action directing completion of the controversial Tellico Dam in Tennessee.

Twice before, the Senate had refused to go along with completion of the dam. But Monday, with Sen. Howard H. Baker Jr. (R-Tenn.) pressuring colleagues to switch their votes, the Senate approved Tellico.

Baker, for his part, as much as dared the president to veto the bill, saying he would work vigorously to override and keep Tellico alive.

The vote on the Tennessee Valley Authority project was 48 to 44 -- with last-seconded vote switches by five Republicans carrying the day.

Earlier, after the House quietly adopted an amendment ordering the completion of Tellico, Andrus and the Office of Management and Budget warned the action was an invitation to a veto.

Andrus, during a meeting with conservation lobbyists yesterday, restated his opposition to Tellico.An Andrus associate said the secretary believes a presidential veto could be sustained easily in Congress.

Although Tellico was not an issue last year, Carter vetoed the same energy and water appropriation bill after objecting on economic and environmental grounds to a number of water projects added by Congress. The veto was sustained in the House.

But TVA's Tellico project on the Little Tennessee River has been a different sort of dispute, involving the Endangered Species Act and its coverage of the tiny snail darter fish.

The Supreme Court held last year that TVA had proceeded illegally with the project by ignoring the imperiled fish. Congress then amended the species act by creating a review panel to adjudicate such controversies as Tellico.

TVA, meanwhile, came up with an alternative development plan that would have avoided use of the $122 million dam, even though it was virtually completed. But the congressionally mandated review panel -- headed by Andrus -- went further, declaring one of its first actions that Tellico was not economical and should be stopped.

The issue resurfaced this summer when the House passed an amendment by Rep. John J. Duncan (R-Tenn.), ordering Tellico completed, notwithstanding any other federal law. The Senate followed suit Monday.

The Little Tennessee River Alliance, a group of farmers and conservationists opposing Tellico, also urged Carter yesterday to veto the bill.

"We're dismayed at the blatant arm-twisting that turned the vote around," a spokesman for the group said.