Its latest intervention is seen by some as a challenge and warning to the president, sworn in barely a week ago.
On President Mursi's orders, the speaker has convened a meeting of parliament on Tuesday.
Crowds were gathering in Tahrir Square ahead of the meeting called for 10:00 (08:00 GMT), in defiance of the military's decision.
The Muslim Brotherhood - which has the biggest bloc of seats in parliament - said it would participate on Tuesday "in a million-man march in support of the president's decision and reinstating parliament".
The military council said it was confident "all state institutions" would respect the law and constitution.
The BBC's Jon Leyne, in Cairo, says the political truce in Egypt appears over.
'Binding and final'
The statement from the Supreme Council of the Armed Forces (Scaf) will infuriate the Muslim Brotherhood, our correspondent says.
Earlier on Monday, the Supreme Constitutional Court rejected the decree issued by Mr Mursi the day before to reconvene the Islamist-dominated parliament.