Telangana Rashtra Samithi, which switched to the National Democratic Alliance side three days ago, has not been called for the meeting, Communist Party of India-Marxist General Secretary Prakash Karat said on Wednesday.
"Leaders of non-Congress, non-BJP will meet here on May 18 to decide the future course of action. BSP will join these discussions where we will explore the possibilities of forming an alternative secular government," he told media persons in New Delhi.
Karat said the Left parties will meet in New Delhi on May 17 which will be followed by the CPI-M's Politburo meeting on May 18 and Central Committee the following day.
On reports about BJP sending feelers to Telugu Desam Party, Karat said he was in touch with TDP chief N Chandrababu Naidu on a "daily" basis. "In fact, it was he (Naidu) who asked me to make this announcement," he said.
"He (Naidu) is the main mover behind the non-Congress, non-BJP combine," Karat said.
On Janata Dal-Secular leader H D Kumaraswamy meeting Congress chief Sonia Gandhi on Tuesday, Karat said former Prime Minister H D Deve Gowda has already clarified his party position.
"He (Gowda) is one of the main movers of the front." When asked about what parties like All India Anna Dravida Munnetra Kazhagam, TDP and JD(S) would do, he said "I can't speak on behalf of all these parties."
Besides BSP, Left parties, AIADMK, TDP, Biju Janata Dal and JD(S) will also participate in the meeting.
Communist Party of India General Secretary A B Bardhan said, "What's wrong in that? She will consult her allies which are the CPI and the CPI(M). Without discussing with us, she will not think of any option", when asked to comment on AIADMK chief Jayalalithaa's statement that her party would take a decision after the poll results in consultation with her allies.
Bardhan also said after the results are out on May 16, the Third Front would get "more numbers" and "will tell the President that we must be given a chance."
The Left parties would meet on May 17, a day after the results come out. The CPI National Executive would meet on May 19 followed by a three-day session of its National Council. The decision-making bodies of Forward Bloc and the Revolutionary Socialist Party would also be meeting on the same days.