Somsak said he has scheduled joint meetings of the House and the Senate until May 11 for the second reading.
As of Wednesday, 10 days had been devoted to the second reading. Somsak said only two more key articles - Article 291/11 and 291/13 - of the amendment bill need to be deliberated.
Late Tuesday night, MPs and senators voted 337 to 50 to approve Article 291/6 of the charter amendment as proposed by the Pheu Thai-dominated vetting panel.
The vote was cast at 11.50pm Tuesday night after a debate that lasted three days.
The article empowers the Parliament president to compile the list of candidates for 22 specialist members of the Constitution Drafting Assembly as proposed by various organisations. The list will be submitted to Parliament for MPs and senators to select the 22 CDA specialist members.
Two parliamentarians abstained while three others were present but declined to press the button to cast any vote.
Somsak said Wednesday that he was worried about the use of improper language by MPs during the debate because it was broadcast live on TV. He said he would remind MPs to use polite language and if his warning went unheeded, he would ask the House ethical committee to investigate the MPs.