CAIRO (AP) ― Egypt’s powerful Islamists on Monday faced a backlash on two fronts as they try to solidify their hold on the country’s politics, as liberal politicians quit a panel tasked with drafting a new constitution to protest its domination by Islamists.

More ominously, the ruling military issued a veiled threat of a crackdown on the Muslim Brotherhood if the group persisted in demands to form a new government.

The warning pointed to a growing possibility of confrontation between the Brotherhood and the military, which emerged as Egypt’s two most powerful institutions since the fall of longtime authoritarian ruler Hosni Mubarak a year ago. For months, they have moved between cooperating and jostling for position.

But the Brotherhood appears to be growing in confidence over its position. The group holds nearly half the seats in parliament, making it the largest bloc ― and its strength grows even more on some issues in which it is backed by the second-largest bloc, the ultraconservative Islamic Salafis.

Together they have been demanding the ouster of the military-appointed prime minister so they can form their own government. The military has staunchly refused. They have also used their strength in parliament to create a constitutional panel with an Islamist majority, giving them the strongest hand in writing the new charter.

In response to the tensions with the military, the Brotherhood’s leader, Mohammed Badie, said in comments posted on the group’s website Monday that it was “quite possible’’ for the Brotherhood to reverse an earlier decision not to field its own candidate in presidential elections due in May.

If the military-Brotherhood quarrel escalates, the transfer of power from the military to a civilian president ― scheduled for before July 1 ― could be in jeopardy. Their dispute could also hand the liberal and secular groups that engineered the 18-day uprising that toppled Mubarak an opportunity to move back to center stage after months on the side.

The independent Al-Shorouq daily said on Monday that several members of the ruling military council have expressed their disapproval of the makeup of the panel in a meeting with Brotherhood leaders. Brotherhood officials could not be reached for comment, but the report was the latest in a series published in the independent media suggesting that relations between the two sides have become so strained that a rapprochement may not be possible any time soon.

Two prominent liberal Egyptian politicians ― independent lawmaker Amr Hamzawy and Christian activist Mona Makram Obeid ― were the first to announce they were pulling out of the 100-member constitutional panel on Monday.

Lawmaker Emad Gad said 11 other liberal politicians have also decided to pull out and were due to formally announce their decision on Tuesday, a day before the body is scheduled to hold its inaugural session. The group include eight members of the panel and three “reserve’’ members, who would serve if a member bows out for any reason. Gad is one of the three reserve members pulling out.

“The entire process is a show to conceal the intention to draft a constitution for a religious state,’’ said Gad, a Christian. “It’s a disgrace to the constitution,” Sherif Samir, a spokesman for the secular Free Egyptians Party, said of the religious slant of the panel.

The controversy surrounding the panel’s makeup drew a guarded reaction from the United States, which has over 30 years regarded Egypt as a key partner in the fight against Muslim militancy.

“We want to see a new constitution for Egypt that upholds democratic values and universal human rights in all of their aspects and provides protections and assurances for the participation and the rights of all Egyptians,’’ U.S. State Department spokeswoman Victoria Nuland told reporters in Washington on Monday.

She said the panel has an “obligation to uphold and defend and protect the democratic rights that brought them to power in the first place, including the universal rights of all groups.’’

Selected over the weekend, the panel includes nearly 60 Islamists and only six women and six Christians. The members were chosen by parliament’s two chambers, where Islamists have a comfortable majority of more than 70 percent.

“I polled those who elected me and the majority of them said they preferred for me to stay on the constituent assembly,” Hamzawy wrote. “I gave the matter a great deal of thought and studied the makeup of the assembly. My conscience told me to pull out.”

Obeid, a former lawmaker and a prominent women’s rights activist, said, “the religious nature and the absence of women are behind my withdrawal from the constituent assembly.’’

The new constitution will determine whether Egypt, a mainly Muslim nation of some 85 million people, will become further Islamized. The charter also will determine whether the decades-old system of a powerful president will be maintained, or instead, an empowered parliament under Islamist domination will set the tone.

The Brotherhood’s spat with the military has its roots in the Islamists’ resolve to fire the military-backed government of Prime Minister Kamal el-Ganzouri, a Mubarak-era politician who is nearly 80.

“The (ruling) military council bears full responsibility for attempts to hinder the process of democratic transition and ... exporting crises to future governments,’’ said a statement by the Freedom and Justice Party, the Brotherhood’s political wing. The party also charged that the military might try to rig the presidential election to install a favorable candidate.

The military hit back with a strongly worded statement on Sunday saying it was unacceptable to question its commitment to turning over power to a civilian government and to a fair presidential election.

It also made a thinly veiled threat of a crackdown against the group by alluding to the mid-1950s, when the Brotherhood was outlawed and its members detained after the group challenged the rule of the military.