(Reuters) -- Richard Lugar, the six-term senator from Indiana struggling to beat back a Tea Party-backed rival in Tuesday's Republican primary, made a last minute appeal for votes by saying his challenger will lose to a Democrat in November.

If he is defeated on Tuesday, Lugar would be the first Senate incumbent of either party to lose so far this election year. He is a key voice in the Senate on foreign policy.

In an email to backers sent Sunday with the subject Your Vote, Lugar, 80, argues a vote for his challenger, Indiana state Treasurer Richard Mourdock, all but guarantees the seat will wind up in Democratic hands on Election Day.

Mourdock enjoys a 10-percentage-point lead over Lugar among likely Republican voters, according to a poll released last week. That was a sharp swing from a poll taken in late March by the same group in which Lugar led, 42 percent to 35 percent.

Lugar, one of the longest-serving U.S. senators, said he understands the frustration of former supporters who have told him they plan to vote for Mourdock, 60, to protest against what is happening in Washington.

But Lugar says that while an independent poll suggests he would trounce the Democratic candidate, Rep. Joe Donnelly, in November, that same poll shows Mourdock would not.

That poll, taken in March, showed Lugar 21 percentage points ahead of Donnelly in a head-to-head matchup in November but had Mourdock and Donnelly essentially tied.

For that reason, both state and national Democrats, including Super-PACs, have been pouring money into the state trying to get Richard Mourdock elected. Democrats understand Joe Donnelly will beat Richard Mourdock, Lugar wrote.

On Saturday, Lugar's campaign manager sent an email to supporters insisting the incumbent's hopes hinged on turnout.

Talk to enough family and friends - fellow Hoosier voters - before Tuesday's primary election to save Dick Lugar and Indiana's Senate seat, the email said.

The winner of Tuesday's primary will face Donnelly, a third-term U.S. representative, in November.

Lugar has received high-profile endorsements from Indiana Gov. Mitch Daniels and Senate colleague John McCain, the 2008 Republican presidential nominee.

Mourdock enjoys the backing of Tea Party favorite and former Alaska Gov. Sarah Palin and former Republican presidential hopeful Rick Santorum.

Indiana conservatives have accused Lugar of losing touch with the state. He was embarrassed earlier this year when officials in one county ruled that he and his wife did not meet residency requirements to vote there.

Conservative critics also say Lugar is too moderate for the state. They attacked him for voting to raise the U.S. debt limit, favoring the 2008 bank bailouts, and supporting President Barack Obama's Supreme Court appointees.

Democrats hold a 53 to 47 advantage in the U.S. Senate.

(Reporting by Nick Carey; Writing by James B. Kelleher; Editing by Greg McCune and Philip Barbara)