Al-Gamaa Al-Islamiya denied Wednesday urging President Mohamed Morsi to accept early presidential elections, underlining his "legitimacy" as an elected leader.
Al-Gamaa Al-Islamiya said it suggested some possible solutions for Egypt's political crisis with some political forces to be announced soon.
The suggested solutions did not include early presidential polls.
Tarek El-Zomor, a senior member of Al-Gamaa Al-Islamiya, had told Reuters that the ultra-conservative group had called on Morsi to accept a referendum on early polls in order avoid bloodshed.
"This peaceful, constitutional transfer (of power) will spare blood," El-Zomor told Reuters by telephone, adding that it would also protect the constitution that was passed into law in December 2012.
He said the army's statement on Monday appeared to presage a coup, but this "can be avoided if the president decides to hold a referendum on early presidential elections."
Al-Zomor, on his Twitter account, said that a referendum on early presidential elections will "preserve the constitutional transition of power and save a lot of efforts."
A statement by the group — a close ally of the president — comes after Morsi gave a speech late Tuesday stating that he would not step down.
Morsi claimed he would remain president not for the sake of power but to protect the legitimacy of the Egyptian constitution, which was drafted and passed during his first year in office.
Morsi proposed an initiative that included forming a new government, holding parliamentary elections within six months, forming a committee to review proposed constitutional amendments, resolving disagreements over Egypt's prosecutor-general, and promoting the inclusion of youth in government.
The opposition rejected Morsi's proposals and called for nationwide protests, including in front of the Qobba presidential palace, where Morsi is now.
Egyptians are counting down until 16:30pm (14:30 GMT) when the army's 48-hour deadline ends. The army gave Morsi and the opposition the deadline to reach an agreement, or else — according to the army's statement Monday — it will take matters into its own hands and propose a 'roadmap' to move forward.
Morsi dismissed the army's statement, saying that no one, either "internally or externally," will interfere in Egypt's domestic affairs.