The call was made by Pheu Thai spokesman Prompong Nopparit on Sunday ahead of the scheduled meeting between the government led by caretaker Prime Minister Yingluck Shinawatra and the EC on Wednesday to discuss the timeframe of the new election.
Mr Prompong said Pheu Thai and the majority of existing political parties had earlier sent a letter to the EC asking it to hold the election in 60 days of a royal decree being issued.
The idea of holding the election on July 20 was solely floated by Somchai Srisuthiyakorn, the EC member in charge of election management.
A quicker election would not be for the benefit of Pheu Thai or other political parties but for the country as a whole, he said.
The EC should listen to the voices of the people, political parties and the international community which say an election is the way out for the country, not only for People's Democratic Reform Committee leader Suthep Thaugsuban or the Democrat Party, Mr Prompong added.