Asa Hutchinson, the former Arkansas governor, who is considering running for the Republican nomination for president, has criticized the loyalty pledge.
Other Republicans who have entered the presidential race include former South Carolina governor and UN ambassador Nikki Haley as well as biotech millionaire entrepreneur Vivek Ramaswamy.
Prominent Republicans who could eventually launch presidential runs include former vice-president Mike Pence, ex-secretary of state Mike Pompeo, and Florida governor Ron DeSantis.
The RNC has scheduled its first presidential primary debate for August.
