By David Dawson

INDIANAPOLIS (Reuters) - Senator Richard Lugar, a six-term incumbent representing Indiana and a leading voice on foreign policy in Congress, trails his Tea Party-backed challenger by double-digits ahead of Tuesday's Republican primary, a poll showed on Friday.

Indiana Treasurer Richard Mourdock, who draws support from the conservative Tea Party movement, leads Lugar by 10 percentage points ahead of Tuesday's primary, the Howey/Depauw Indiana Battleground Poll showed.

If defeated, Lugar, the senior Republican on the Senate Foreign Relations Committee and a leading voice on stemming the spread of nuclear weapons, would be the first Senate incumbent to lose his seat this election year.

The poll conducted this week showed Mourdock with 48 percent support among likely Republican primary voters compared to Lugar's 38 percent. This was a sharp swing from a poll taken in late March by the same group in which Lugar led 42 percent to 35 percent.

"It certainly looks as if the momentum has shifted toward Richard Mourdock," Republican pollster Christine Matthews wrote of the poll she conducted with Democratic pollster Fred Yang, political analyst Brian Howey and Depauw University.

The winner of Tuesday's primary faces Democratic U.S. Representative Joe Donnelly in the November general election.

Polls have shown Lugar easily beating Donnelly, but a tight race if Mourdock, 60, is the Republican nominee.

Democrats hold a 53 to 47 advantage in the Senate and a Lugar defeat in the primary would improve Democrats' chances of retaining control of the chamber.

Lugar, 80, has received high-profile endorsements from Indiana Governor Mitch Daniels and Senate colleague John McCain, the 2008 Republican presidential nominee.

Mourdock, who already has the backing of Tea Party favorite and former Alaska Gov. Sarah Palin, was endorsed by former Republican presidential hopeful Rick Santorum on Friday.

Indiana conservatives have accused Lugar of losing touch with the state. He was embarrassed earlier this year when officials in an Indiana 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.

They describe Lugar as Obama's favorite Republican. McCain did a radio spot in which he touted Lugar's conservative credentials and branded the charge that Obama and Lugar were close as "ridiculous."

The poll of 700 likely Republican primary voters was conducted on April 30 and May 1, and had a margin of error of plus or minus 3.7 percentage points.

(Editing by Andrew Stern, Greg McCune and Stacey Joyce)