United Progressive Alliance president Sonia Gandhi has rejected the Third Front's plea for consensus on a second term for President APJ Abdul Kalam.
Leaders of the Third Front will meet Left leaders Prakash Karat and A B Bardhan and Nationalist Congress Party chief Sharad Pawar on Thursday.
The leaders of the newly-formed eight party grouping, United National Progressive Alliance, had also sought time from Sonia.
UNPA leaders led by TDP supremo Chandrababu Naidu called on the President to persuade him to contest for a second term in office.
After the 45-minute-long meeting, Naidu said Kalam was "willing to consider contesting for a second term provided there is certainty among political parties," but did not elaborate on what he meant.
Meanwhile, the President has said he is willing to "wait for a few days for certainty".