Egypt's powerful army called on Tuesday for President Mohamed Morsi and opposition political parties to meet to resolve the dire crisis splitting the country.

General Abdel Fattah al-Sissi, the country's armed forces chief and defence minister, made the appeal in a statement posted on the military's official Facebook page.

"The chief of the military and defence minister calls for a meeting for the sake of Egypt that will bring together national partners in the presence of the president of the republic," the statement said.

The invitation was extended to the government, judges and to "all political forces" and movements, it said.

The proposed venue for the talks was a military sports complex in northeast Cairo.

Sissi made his call as rival protesters gathered in Cairo for mass rallies for and against a constitutional referendum called by Morsi for Saturday.

The army has orders from Morsi to use temporary police powers to protect state institutions, following clashes in the capital last week that left seven people dead and hundreds hurt.

The army, which ruled Egypt between the February 2011 ouster of autocratic leader Hosni Mubarak and the June 2012 election of Morsi, has tried to remain neutral in the crisis but has warned it will not allow the situation to worsen.

At the weekend, the military demanded talks between the two sides, but the opposition said no dialogue was possible unless Saturday's vote is called off.