"Some think the way to beat the Democrats in November is to be more like them. I could not disagree more," the one-time Tennessee senator says in remarks he is to deliver before the Conservative Party of New York.
"I believe that conservatives beat liberals only when we challenge their outdated positions, not embrace them. This is not a time for philosophical flexibility, it is a time to stand up for what we believe in," Thompson adds.
He doesn't mention Giuliani's name in excerpts made available to The Associated Press, but he's clearly trying to draw a contrast with the rival who's leading in national Republican polls.
Giuliani was once a Democrat. Unlike Thompson, the New Yorker backs abortion rights and gay rights. And, the ex-mayor's central argument for Republicans to nominate him is that he gives them the most likely shot to win in the general election.
Ahead of Thompson's speech, Giuliani's campaign arranged for several deputy mayors who served in his administrations to hold a news conference in Times Square later Monday to promote his success in reducing crime, overhauling welfare and cutting taxes.
"Some candidates talk the talk about Republican principles. Others actually have a proven track record of governing according to Republican principles. Rudy Giuliani has that record," Randy Mastro, a deputy mayor in Giuliani's first term told the AP before the news conference.
With voting beginning in under three months, Thompson is trying to win the support of conservatives who are pivotal in GOP primaries.
"With me, what you see is what you get. I was a proud conservative yesterday, I remain one today, and I will be one tomorrow," Thompson says.
He touts his eight-year Senate tenure and boasts of working to further the conservative causes of smaller government, lower taxes, less regulation and conservative judges.
In fact, while he was seen as a reliably conservative vote in the Senate, he sometimes strayed from the party line and focused more on investigating than legislating.
Conversely, Giuliani voted for Democratic presidential nominee George McGovern in 1972. As a Republican mayor, he broke from the GOP and endorsed Democratic Gov. Mario Cuomo in an unsuccessful race for a fourth term. In his own two terms as mayor, Giuliani staunchly supported abortion rights, gay rights and gun control - and also was left-of-center on a host of other issues.
He also has had a rocky history with the Conservative Party of New York.
In his first mayoral race in 1989, Giuliani ran as a Republican but sought and won the Liberal Party's endorsement, too. He lost but ran again in 1993, that time winning with the Liberal Party's backing.
Thompson's address to the Conservative Party will be his first public event since participating in his first presidential debate in Michigan last Tuesday. He was scheduled to be in New Hampshire late last week for a fundraising breakfast for Manchester Mayor Frank Guinta, but he canceled his trip. Aides say he also plans stops this week in Washington, Georgia and Florida.