Egypt's interior ministry on Saturday renewed its appeal to supporters of ousted president Mohamed Morsi to end their ongoing sit-ins in Cairo and Giza, promising to provide them with protection is they choose to leave.

"The ministry understands that a big number of the protesters want to leave and return to their homes but fear being followed by security apparatuses or fear the threats of the sit-in’s organisers if they leave...we reiterate our promise to protect the protesters and ensure their safety," the ministry said in a statement posted on its Facebook page.

The sit-ins at Nahda Square in Giza and outside Rabaa Al-Adawiya mosque in Cairo have been ongoing for several weeks, drawing tens of thousands of protesters. The cabinet on Wednesday authorised the interior ministry to disperse both demonstrations, but protesters have so far defied entreaties to leave the sites.

"The ministry of interior and the Egyptian people know that the protesters are being brainwashed by the organisers of the sit-ins who do not let them know the latest news, except that which they announce from their stages in order to keep them as hostages," said the statement, adding that the protesters were being used by the Muslim Brotherhood for political gains in the negotiations process.

The interior ministry further warned protesters that if they continue their sit-ins they could be found “legally accountable for the crimes committed during the sit-ins incriminated by law including murder, torture, kidnap, possession of weapons and incitement.”

Critics have alleged that incidents of kidnapping and torture have occurred at both the Rabaa and Nahda sit-ins, and have said that the protesters possess weapons.

Amnesty International issued a statement on Friday saying eyewitness accounts reveal that incidents of torture had taken place at both sit-ins, carried out by Brotherhood members against political rivals. The rights group urged an investigation.

The ministry of interior also warned urged protesters in its Saturday statement to choose a “safe exit” which would be available to those who “have not committed any crime.”

The interior ministry had on Thursday made a similar call to pro-Morsi protesters to clear the sit-ins.

However, Colonel Ahmed Ali told the London-based Arabic language newspaper Al-Sharq Al-Awsat on Friday that: "there has been a misunderstanding that the [pro-Morsi] vigils would be dispersed a day later (after the cabinet announced it had authorised the interior ministry to end the protests)".

Ali affirmed right to peaceful protest but stated that the pro-Morsi sit-ins have “departed from the peaceful context” and shown a “tendency towards violence” which is concurrent with “terrorism” and recurrent rocket attacks in the Sinai Peninsula.

Dozens of security personnel have been killed in armed attacks on state buildings and outposts in Sinai since Morsi’s ouster on 3 July.

He went on to affirm that the pro-Morsi vigils are armed, citing deadly clashes with security and army officers resulting from marches and rallies in which weapons were used, "leaving deaths on both sides."

Meanwhile, Vice President for Foreign Affairs Mohamed ElBaradei said during an interview with the Washington Post published on Friday that he still hoped that a political solution could be reached, and that he would gladly lead talks with Morsi’s Muslim Brotherhood to prevent more bloodshed.

"There hasn't been an organised dialogue between them (Brotherhood leaders) and the government. There's a lot at the civil society level, but once the violence is out of the way, we’d like to get some dialogue," ElBaradei said.

The liberal politician said that a safe exit for all Muslim Brotherhood leaders is "on the table," including deposed president Mohamed Morsi.

"There are charges levied against him. I think once we get the violence down and start a dialogue, a lot of these things could be checked," ElBaradei said.

A week ago, a top Egyptian court ordered the detention of Morsi for 15 days pending investigations into his suspected collaboration with Palestinian Islamist group Hamas, an ideological offshoot of the Brotherhood.

Secret negotiations have reportedly started between Egyptian state bodies and the Muslim Brotherhood to avoid an escalation in Egypt’s current political crisis, reported Ahram’s Arabic website on Friday. Communication between the Muslim Brotherhood and the state bodies started late on Thursday and continued into Friday morning.

The Brotherhood representatives called on the state to release some of the organisation’s leading figures as a goodwill move, according to Ahram’s sources. The state for its part called on the Brotherhood to cease promoting hate speech and discourse about war and martyrdom at the Nasr City sit-in and to cease its spontaneous protests.

On Saturday, US Deputy Secretary of State William Burns met with Egypt’s Foreign Minister Nabil Fahmy. Burns is expected to hold meetings with Egyptian political leaders concerning the importance of avoiding violence and facilitating a peaceful and inclusive political process.

Muslim Brotherhood spokesperson Gehad El-Haddad said that a delegation of the National Coalition to Support Legitimacy, an Islamist pro-Morsi coalition, will also be meeting Burns.

However, he said that the meeting with Burns “aims to insist on restoring the constitutional legacy and rejecting the coup, as well to insist on keeping the public mobilisation to achieve this."

Burns is not the only foreign figure visiting Egypt in an attempt to close the gap between rival political camps. EU Foreign Policy Chief Catherine Ashton was in Egypt last week holding meetings with political figures from the rival camps. Ashton visited Morsi, who has been detained at an undisclosed location since his ouster 3 July.

European Union Special Representative for the Southern Mediterranean Bernardino León also arrived to Egypt Wednesday at the request of Ashton, for further talks with pro-Morsi leaders and leaders of the transitional government. He also attended the meeting with Burns and Fahmy at the Egyptian foreign ministry headquarters.