The debates would take place the Rio Grande Valley, San Antonio, Dallas-Fort Worth, El Paso, Houston and Lubbock.
Abbott, who announced Monday that he had accepted two debate invitations from media outlets — one in McAllen and one in Dallas — did not appear immediately receptive to the proposal.
“The debate about debates is over,” an Abbott campaign press release said. Campaign spokesman Avdiel Huerta declined to clarify.
In the proposal, Davis called for at least two issue-specific debates on education and economic opportunity. Additionally, she called for one debate to be simulcast in English and Spanish.