The Election Commission (EC), meanwhile, said it would continue planning for nationwide polls and would leave it to politicians to sort out their problems.
NSPRT adviser Nittithorn Lamluea commended the Democrat Party leader for proposing a 10-step plan to find a solution to the political turmoil. But he said it lacked details about measures to end former prime minister Thaksin Shinawatra's political influence, the main goal of his group.
Mr Nittithorn also dismissed Mr Abhisit's idea of allowing politicians to get involved in reforms as anti-government demonstrators opposed the idea.
He said the protesters wanted politicians to take a pause while real people work on the reforms.
The NSPRT, a hardline ally of the People's Democratic Reform Committee (PDRC), has vowed to fight on until all Shinawatra family members and their network end their political roles, he added.
Election commissioner Somchai Srisuthiyakorn said his agency would continue to make preparations for a general election on July 20 as planned as the date had been agreed with the caretaker government led by Yingluck Shinawatra.
The EC will leave the political problems for the government and the parties opposing it to sort out, he added.
A royal decree for the July 20 polls will be sent to the caretaker government for approval on Tuesday.
"If the government sees the benefit of the (Abhisit) proposal, it should make its position clear to the public and call a new meeting with the EC to delay the plan to forward the decree to His Majesty the King," he said.
The decree still needs the King's endorsement after it passes the cabinet.
Mr Abhisit warned of possible bloodshed if the government and PDRC could not find a common ground to end their standoff.
His plan includes the resignation of caretaker Prime Minister Yingluck Shinawatra to pave the way for the setting up of an interim administration with a premier acceptable to all sides appointed by the Senate.