All but one of the 17 Republicans vying for the party's presidential nomination have made the cut so far for the next candidates' debates hosted by CNN, the network said on Tuesday in a decision that could leave former Virginia governor Jim Gilmore on the sidelines.

CNN and the Ronald Reagan presidential library, which is co-hosting the 16 September debates, said invitations have been sent by former first lady Nancy Reagan to 16 candidates who meet their criteria. All but Gilmore "have qualified thus far and have received invitations", they said in a statement.

Earlier this year CNN said candidates must meet certain criteria, including an average of 1% of support in three recent national polls. The network's latest poll showed Gilmore at the bottom of the pack with less than 1%.

"Additional candidates will receive invitations if they meet all of the previously released debate criteria," CNN and the library said.

Like last week's Republican presidential debates hosted by Fox News, the CNN event will actually be two debates – dividing the crowded Republican field into two groups, with one featuring the top 10 candidates.