A group of high-profile Democratic veterans is urging a Wisconsin Republican Senate candidate to apologize for comments he made about military vets who support the Democratic Party. 

GOP candidate and Marine veteran Kevin Nicholson said last week that he questions the "cognitive thought process" of Democrats who served, saying "they're signing up to defend the Constitution that their party is continually dragging through the mud."

In a letter, Democratic figures including former Georgia Sen. Max Cleland — a Vietnam veteran and triple amputee — write that Nicholson's comments do "not just disrespect our nation’s veterans, but crudely do so as a means to advance his own political career."

"Mr. Nicholson knows that military service crosses party lines," they write. "It is beneath any serviceman or woman to politicize veterans and assert that patriotism is limited to members of one political party."

Other signers include U.S. Senator Tammy Duckworth, Rep. Seth Moulton and former Missouri Senate candidate and Democratic activist Jason Kander.

Nicholson, who is competing in a primary against Leah Vukmir, has come under bipartisan criticism for the remarks. A group of Republican veterans who support Vukmir has also called for him to apologize. 

Nicholson has said he stands by the remarks, saying that he "won't back down." 

The winner of the August 14 GOP primary will take on Democratic incumbent Tammy Baldwin.