Cairo (CNN) -- The military council that runs Egypt and an Islamist party that has done well in parliamentary elections accused each other Thursday of plotting a dictatorship. Leaders also sparred over plans for drafting Egypt's constitution, a key battlefront in the nation's political future. "We will not allow a dictatorship and we do not want to remain in power, but we do want a civil government representing all Egyptians without marginalizing any minorities," said Lt. Col. Amr Imam, a spokesman for the Supreme Council of the Armed Forces, which has run the country since a popular uprising ousted former President Hosni Mubarak in February. Imam said the first-round results do not "represent all factions of the society, like the Coptics for example," in reference to the country's largest Christian sect. His remarks seemed aimed at Islamist parties that have done well in the first round of parliamentary elections, including the relatively moderate Muslim Brotherhood. Its Freedom and Justice Party has said it had won 34 seats in early parliamentary elections, while the more hardline al-Nour party said it had won five. The Muslim Brotherhood has pledged to respect minority rights and work with liberal parties, while al-Nour, a Salafist party, supports broader application of its interpretation of strict Islamic law in Egypt. Imam's assessment came a day after similar comments a high-ranking military general reportedly made during a small briefing with international reporters. According to media reports, Gen. Mukhtar al-Mulla said the election results did not fully represent the public and noted that the military would increase its role in the drafting of Egypt's constitution. A spokesman for the Muslim Brotherhood's party attacked al-Mulla's reported comments, calling them "almost humorous and leaning towards calling for a new dictatorship." "Talk of parliament not representing the people could takes us back to medieval times," said Ahmed Abu Baraka. "I don't think he was fully aware of what he was saying and his statements will not pass unnoticed." On Thursday the deputy director of the Muslim Brotherhood's party said they would pull out of participating in a government advisory board after learning that military officials wanted the board to help draft Egypt's constitution. "We joined the first sessions on the basis that this council would assist in the management of the interim period, but then realized that the Supreme Council of the Armed Forces has other plans for this advisory board, which included participation in the drafting of the constitution, which basically deprives the parliament of its authority," Dr. Esam al-Erian said. In addition to sharp criticisms they drew from Islamists, the military leaders' remarks have further fueled fears that the military does not intend to cede power, said Shibley Telhami, a professor at the University of Maryland and senior fellow at the Brookings Institution. "They've played into the hands of those who worry that the military institution does not intend to relinquish political control," Telhami said. Such comments make it appear "as if the military didn't quite understand what democracy means," he said. Previously, officials had agreed that whoever won the parliamentary elections would appoint the committee to draft the constitution, said David Schenker, director of the Program on Arab Politics at The Washington Institute for Near East Policy. "I think the military had some time to rethink that decision. ... They're trying to change the ground rules," Schenker said. "The military is trying to protect its privileged role in society. It doesn't want to be accountable to civilian authority." Islamists, empowered by their election victories, also are trying to increase their role in drafting the constitution, Telhami said. "They smell the power and they want to use it to play a bigger role," he said. "That's really where the tug-of-war is a the moment," he said. Despite the criticisms, Telhami said, military officials may be making an important point. "There is a point to be made that they did not make as well as they could have, which is that the constitution is a document that is far bigger than any single parliament. ... It has to be written with a lot more in mind than just the short-term political interest of the community," he said. He pointed to the U.S. Constitution as an example. "Most Americans would feel highly uncomfortable if a new constitution of the United States of America today was written by our Congress. ... There was an understanding that the Constitution is not something that should be contingent on a single episode of politics," Telhami said.