Udomdej Ratanasathien, the chairman of the coalition coordination committee on parliamentary affairs, said the second reading could be extended from April 18 and 19 to April 22 if the initial schedule does not provide enough time for MPs and senators to debate.
The second reading resumed Wednesday after the debate ended abruptly last week following the tsunami scare.
After the second reading, parliamentarians must wait 15 days before casting a vote whether to approve the charter amendment bill in the third reading.
Parliament President Somsak Kiartsuranon said Wednesday that the third reading of the charter amendment bill will be held on May 8.
Udomdej said if the second reading is extended to April 22, there would still enough time to comply with the 15-day wait period.
Udomdej said the coalition was ready to be flexible on the timeframe and the whips have asked Pheu Thai MPs to refrain from protesting against the opposition too often.
Udomdej said Pheu Thai MPs should be patient so that the meeting can proceed smoothly.
The amendment is to change Article 291 so that a new constitution drafting assembly can be set up to draft a new charter.