The liberal Free Egyptians Party has described Monday's interim constitutional decree as "highly disappointing," Al-Ahram Arabic news website reported.
The party approves of the "principle of the roadmap" in the decree, but has doubts concerning some articles.
"The decree was not discussed with the different political forces," party spokesperson Shehab Wageeh said.
Two articles caused the party particular concern.
Article one, which says Islam is the official religion of the country – and was a source of contention in the drafting of the 2012 constitution - was included in the decree to "appease a political party [i.e. the ultra-conservative Nour Party] that has been trying to impose its vision on society," Wageeh said.
"Article One ignores the will of the people who took to the streets on 30 June to denounce parties formed on the basis of religion," Wageeh stated.
"The powers of the president [provided in the constitution] are excessive, and overshadow the prime minister's authority," he said.
The president's authority includes appointing the prime minister and all the ministers.
The Rebel campaign, which organised a petition and mass protests against Mohamed Morsi, said it was working with Mohamed ElBaradei on amendments to the constitution decree, which took it "by surprise."
Ultra-conservative Al-Gamaa Al-Islamiya rejected the constitutional decree and insisted that Mohamed Morsi return to power.
Mansour was appointed Egypt's interim leader on Thursday after the army, with the support of nationwide protests, ousted Morsi.