The ruling Left Front and Trinamool Congress even declared their candidates the same night, while the Congress and the BJP would do so on Wednesday.
The EC on Monday announced November 19 as the date for Barjala and Khowai by-polls.
Ahead of the 2018 polls in Left-ruled Tripura, the crucial November by-polls are set to be a multi-pronged contest, giving advantage to the ruling Left.
The Trinamool Congress (TMC) had urged all opposition parties to field united candidates for the by-polls, to defeat the Communist Party of India-Marxist (CMI-M)-led Left Front.
"We appeal to all opposition parties to support the TMC candidates to prevent division of opposition votes in both seats," TMC leader Sudip Roy Barman said on Monday night.
Barman, who led a split in the main opposition Congress recently, was accompanied by TMC state President Surajit Datta while making the appeal.
He said: "To free Tripura from the clutches of CPI-M dominated Left Front, the opposition must unite."
The TMC has fielded former Minister Prakash Das in the Barjala seat and Manoj Das, a former CPI-M leader, in the Khowai constituency.
A large number of Congress leaders, including Das and six party legislators led by Barman, recently quit the Congress protesting the party's alliance with the CPI-M led Left Front in West Bengal polls.
Rejecting the TMC appeal, Congress said that TMC itself destroyed the option by unilaterally declaring their own nominees in both seats.
"Before announcing their candidates the TMC should have discussed. We would declare our candidates on Wednesday," Tripura Congress Vice President Tapas Dey told reporters.
The Left Front also declared their aspirants -- youth leader Jhumu Sarkar in Barjala and district party secretary Biswajit Datta in Khowai.
Before leaving for Delhi, BJP state unit President Biplab Deb told IANS over phone that names would be declared on Wednesday, after holding discussions with the central leadership.
The Barjala assembly seat fell vacant after the Congress MLA Jitendra Sarkar resigned on June 6 following internal feud, and Khowai seat became vacant after the death of veteran CPI-M legislator Samir Deb Sarkar.
In all 39,007 electorate, including 18,935 female, will be eligible to vote in the Barjala seat, while 39,400 voters, including 19,436 women, will cast votes in Khowai.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)