Abhisit and Suthep have been accused of mishandling the bloody crackdown on supporters of the red shirts’ United Front for Democracy against Dictatorship.
At least 99 people were killed over a two-month period.
Parnthep said Abhisit and Suthep must either make their clarifications in person or in writing by Wednesday.
He said if the men want to use witnesses in an attempt to bolster their cases, the NACC will scrutinise the request under the law and determine if it is necessary to the case.