Former President Donald J. Trump said again on Wednesday night that he would not agree to a second debate with Vice President Kamala Harris, as the noon Eastern time Thursday deadline for his response to CNN’s proposed debate approached.

Ms. Harris had accepted CNN’s offer to debate on Oct. 23. Fox News had also extended an offer on Wednesday for a debate this month.

Mr. Trump insisted on his social media site that Ms. Harris wanted a “rematch” because she lost their first meeting, despite polls that suggested otherwise, finding that most respondents thought Ms. Harris had performed better. He also repeated his suggestion that it was too late to debate again because voting had already begun, though debates in past presidential elections have often been held in mid- to late October.

Mr. Trump also claimed that he was “leading in all swing states,” even though polling averages show him leading in some and Ms. Harris leading in others, with the race very close in all of them.