Egypt's first democratic parliamentary elections look set to be postponed until November, amid a growing standoff between the ruling military council and protesters who believe their revolution is being betrayed.

The vote was initially scheduled to take place in September, causing concern among many nascent political parties who claim they have not had enough time to prepare since the fall of the former president Hosni Mubarak in February, which ended more than half a century of one-party rule.

Many activists argue that an early poll would only benefit those forces which already boast a strong organisational capacity – namely the Muslim Brotherhood and local remnants of Mubarak's NDP party – and some have called for a new constitution to be written before any parliamentary ballot takes place.

This week, against a backdrop of nationwide protests against its handling of the post-Mubarak transition period, the Supreme Council of the Armed Forces (SCAF) acknowledged for the first time that a delay in elections might be necessary.

"Procedures for a parliamentary election will begin in September, possibly the middle of the month. That will involve registration of candidates," an army source told Reuters. "Then there will be a campaigning period … This could take the voting till after September, possibly November."

The military's policy shift on the issue of election scheduling came as a public occupation of Cairo's Tahrir Square entered its sixth day and other protests continued to erupt across the country. On Wednesday, the Mogamma building, Egypt's administrative nerve centre, finally reopened after having been shut for days due to the ongoing sit-in. However roads around Tahrir are still closed off and under the control of protesters, while security forces remain nowhere to be seen.

On Tuesday, SCAF offered its first formal response to the recent grassroots challenge to its legitimacy, through a televised statement by the council's spokesman General Mohsen el-Fangari. The statement – which adopted a paternalistic tone and threatened "anyone seeking to disrupt public order" – was met with furious jeers from protesters in several cities. In scenes reminiscent of Mubarak's final days when the dictator made a series of poorly-received public speeches in an effort to cling on to power, many demonstrators expressed their deliberate disrespect to el-Fangari by holding aloft their shoes during the address.

Soon after the statement ended thousands of demonstrators surged out of Tahrir and towards the nearby parliament building and cabinet office, which are being guarded by the military, to express their dissatisfaction with SCAF and the country's de facto leader, Field Marshal Mohamed Hussein Tantawi. Chants of "the people want the downfall of the Marshal" and "we're not leaving, he is leaving" rang through the streets, but violence was avoided.

"The situation is very, very tense," Mamdouh Hamza, a civil engineer and prominent dissident, told the Guardian. "The military council is angry, but the Egyptian people are twice as angry. SCAF have to have a change of policy, they simply cannot carry on in this way."

In common with many protesters, Hamza identified the glacial pace of trials for those accused of corruption and unlawful killing as the key source of current discontent on the ground. He also condemned the interim government for dragging its heels on compensation for those left dead or wounded in this year's anti-Mubarak uprising, and said the current authorities were "completely ineffective" when it came to implementing revolutionary demands.

In a later press conference, SCAF appeared to adopt a more conciliatory position, insisting that the military had no plans to use violence against "law-abiding" citizens and claiming that suggestions to the contrary "hurt the feelings of the armed forces, which took the side of the people from the very beginning." But the council also claimed that "all options were open" in dealing with those obstructing the normal functioning of the state.

The military also announced it had accepted the resignation of deputy prime minister Yehia el-Gamal, one of several cabinet members that protesters have campaigned against due to their links with the Mubarak regime.

Hamza – who some revolutionaries have nominated as a potential interim prime minister – said that despite the limited concessions, SCAF remains badly out of step with public opinion. But, in contrast to many protesters, he also insisted that forcing the military out of the political process altogether is not the answer.

"If every married man divorced his wife as soon as they had an argument, we'd have no families left," he argued. "We have to get SCAF and Tantawi acting in unison with our demands, but calling for them to go completely means calling for the destruction of the state. We have to hold on to the system we have – our army, our police, our judges – and we have to make it correct, not destroy it."