The Constitution Court has decided to give MPs and senators who signed to support amendments to the charter more time to explain their stance.
The court Wednesday extended the deadline it has given the group by 15 days, as it prepares to hear a petition against the changes.
Some of the lawmakers have defied the court by refusing to say why they want change, though the court says this is not the reason it is extending the deadline.
The first deadline expired on April 26. None of the Pheu Thai MPs who back the changes now before parliament have sent in an explanation as requested, in line with a party resolution.
Red shirts have gathered in front of the court for the past week, demanding that the judges step down over the petition row.
They oppose the court's decision to accept a petition that argues the charter amendment bill passed at its first reading in parliament is unconstitutional.
The Pheu Thai Party said the court's decision interferes with the work of the legislative branch.
Constitution Court spokesman Pimol Thampitakpong announced the new deadline Wednesday. He said the judges had decided to give the 312 MPs and senators who signed to support the amendments to Section 68 another 15 days to explain their stance.
However, Mr Pimol claimed the extended deadline was in response to a request by 46 senators who asked for more time to prepare an explanation.
The court would proceed to consider the petition against the rewrite of Section 68 after the deadline, with or without the explanation from the politicians, he said. "If they don't submit the explanation by the extended deadline, it means they have no objections to raise and the court will follow the due process," Mr Pimol said.
While 46 senators were pleading for more time, the Pheu Thai Party decided to challenge the court's authority.
Mr Pimol said the court judges also agreed by a margin of 5 to 3 to accept for consideration a similar petition by appointed senator Somjet Boonthanom seeking its ruling on the attempt to amend Section 68.
Before it considers this petition, the court would ask the same group of MPs and senators to explain why they wanted the change. They also have until May 15 to explain.
In his petition, Gen Somjet claimed the amendment to Section 68 would do away with the people's right to directly lodge a complaint with the court.
Section 68 allows people to complain directly to the court over acts deemed harmful to the constitutional monarchy.
The amendment would require complaints to be made first with public prosecutors.
Mr Pimol said the court did not issue an injunction halting the amendment process as requested by the senator because there were no grounds for it.
In another development, the charter court also decided to postpone consideration of a petition by Pheu Thai MPs seeking its ruling on the parliamentary status of opposition leader Abhisit Vejjajiva.
The petition seeks to strip Mr Abhisit of his status as an MP, based on Defence Minister ACM Sukumpol Suwanatat's order to strip Mr Abhisit of his acting sub-lieutenant rank for dodging the draft.
He also retroactively nullified Mr Abhisit's appointment as a lecturer of the Chulachomklao Royal Military Academy 25 years ago.
"It is an important matter that requires a further review. The judges decided they would save it for their next meeting which has yet to be scheduled," Mr Pimol said.
Charter court president Wasan Soipisut did not take part in the meeting. Mr Wasan had taken sick leave and Charoon Intajarn presided over the meeting.
The red shirts Wednesday stepped up the pressure against the judges. Charn Chaiya (Noom Korat), and Sornrak Malaithong, called on 100,000 red shirts to converge on Monday to protest against the court.