They accused the Centre for the Administration of Peace and Order (Capo), which on Thursday urged the government to seek the King's advice if the cabinet is removed, of attempting to interfere with the work of independent agencies.
The Capo statement had also warned the court and the NACC against bias and double standards in their handling of cases against Caretaker Prime Minister Yingluck Shinawatra.
Ms Yingluck is accused of breaching the charter in her transfer of National Security Council secretary-general Thawil Pliensri in 2011, and of dereliction of duty over her role in the rice-pledging scheme.
The Constitutional Court on Friday issued a statement denying accusations by Capo that the court would "rule beyond the constitution" to disqualify Ms Yingluck and her cabinet.
It said the Capo statement is tantamount to interfering in the work of the charter court.
The court accused Capo of speculating on the future and of making veiled threats, adding that the security agency was acting far beyond the scope of its authority.
The court also insisted it rules on cases in line with the law and the constitution, and does so in the name of His Majesty the King as stipulated by Section 197 of the charter.
If Capo's actions adversely affect court proceedings, the charter court said it will consider taking legal action against the agency.
The charter court will decide on Wednesday whether to allow Ms Yingluck another 15-day extension to defend herself in the Thawil transfer case.
If the court rules against Ms Yingluck in the case, she faces the prospect of being stripped of her powers as premier, a move which some legal experts believe would also disqualify her entire caretaker cabinet.
NACC secretary-general Sansern Poljiak also released a statement yesterday, accusing Capo of trying to pressure the anti-graft body into making a judgement in favour of the government.
Mr Sansern said the NACC's investigation of Ms Yingluck complies with the rule of law, and dismissed allegations of bias against the government.
The NACC is not discouraged and will not shirk its legal duty even when facing threats and acts of aggression from some groups, Mr Sansern added.
Meanwhile, Ms Yingluck insisted the country will not slide into a political power vacuum if she is stripped of her premiership.
She said a political power vacuum is not possible, as one of her deputies will continue to act on her behalf if she cannot perform her duties as prime minister.
Ms Yingluck said the law states that important positions at any state agency cannot be left vacant, and efforts must be made to fill those vacancies.
Responding to calls by anti-government groups for Section 7 of the constitution to be invoked pave the way for a "neutral" prime minister to be installed, Ms Yingluck said there are many differing views on whether such a move would be possible.
Election Commission chairman Supachai Somcharoen also said yesterday that Capo had no authority to order the EC to speed up its efforts to hold a fresh general election.
Speaking on behalf of Capo, Royal Thai Police deputy spokesman Krissana Pattanacharoen explained that the agency had been required to issue the statement on Thursday because it had obtained information indicating possible violence in areas under its jurisdiction.
Pol Col Krissana said violence could occur as a result of planned rallies by the People's Democratic Reform Committee and the United Front for Democracy against Dictatorship. The rival groups plan to stage demonstrations to coincide with the NACC and charter court rulings.
Democrat Party leader Abhisit Vejjajiva also accused Capo of overstepping its authority and of provoking conflict with independent bodies.
Mr Abhisit said Ms Yingluck, who established Capo to deal with anti-government protests, should consider dissolving the agency because it has failed to carry out its responsibilities properly.
He also warned the government against trying to seek His Majesty the King’s advice if the charter court rules to disqualify Ms Yingluck and her cabinet.
In the event the entire cabinet is disqualified, Mr Abhisit said he did not think the disqualified members would have any legal status to seek His Majesty's advice.