John Kasich, Carly Fiorina, Marco Rubio, Ben Carson, Donald Trump, Ted Cruz, Jeb Bush, Chris Christie, Rand Paul

Republican presidential candidates, from left, John Kasich, Carly Fiorina, Marco Rubio, Ben Carson, Donald Trump, Ted Cruz, Jeb Bush, Chris Christie, and Rand Paul take the stage during the CNN Republican presidential debate at the Venetian Hotel & Casino on Tuesday, Dec. 15, 2015, in Las Vegas. (AP File Photo/Mark J. Terrill)

DES MOINES, Iowa -- Kentucky Sen. Rand Paul and former technology executive Carly Fiorina will not appear on the primetime debate stage when the Republican Party's 2016 presidential class faces off later this week in South Carolina.

Debate host Fox Business Network announced the debate lineup Monday evening, dealing a blow to both candidates three weeks before Iowa's leadoff presidential caucuses. Just seven candidates -- the smallest Republican group so far -- will be featured in Thursday's 9 p.m. ET main event, based on criteria established by the network that relied on recent polls.

Real estate mogul Donald Trump, the leader in most recent polls, will again appear center stage in the debate. He'll be joined on stage by Texas Sen. Ted Cruz, Florida Gov. Marco Rubio, retired neurosurgeon Ben Carson, former Florida Gov. Jeb Bush, New Jersey Gov. Chris Christie and Ohio Gov. John Kasich.

Paul and Fiorina were invited to participate in a 6 p.m. ET "undercard" debate, although Paul said he would skip the second-tier faceoff.

"An artificial designation as being in the second tier is something we can't accept," he told CNN on Monday. "I won't participate in anything that's not the first tier."

Before the lineup was announced, Paul strategist Doug Stafford said: "This race is hitting its final stretch and Rand Paul is a serious contender for the nomination. He expects to be on the stage this week because he has qualified to do so and because he has a top-tier campaign." Stafford noted that Paul has qualified for primary ballots in every state, has more than 1,000 precinct captains in Iowa, and has a 500-person leadership team in New Hampshire.

Fox Business Network said the primetime lineup would include the top six candidates in the five most recent national polls in addition to any candidate in the top five in either Iowa or New Hampshire.

Others invited to the undercard event include former Arkansas Gov. Mike Huckabee and former Pennsylvania Gov. Rick Santorum.