Egypt's Muslim Brotherhood announced later on Sunday that its candidate Mohammed Mursi is advancing in several provinces, hours after the ruling military council issued an amended constitutional document handing it sweeping powers, including legislative control, after a court ruled the elected parliament invalid.
Mursi had 61 percent of the 1.4 million votes counted so far, compared to 39 percent for Shafiq, Mursi campaign official Yasser Ali told a news conference less than two hours after polling stations closed at 10 p.m. (20:00 GMT).
There are about 50 million eligible voters. Turnout was 46 percent in the first round, when neither candidate received more than a quarter of the votes cast.
A Shafiq campaign official dismissed the Brotherhood's count, saying his candidate was ahead but gave no numbers.
Each campaign is allowed to have representatives in polling stations to watch the count.
Meanwhile, an amended constitutional document, a copy of which was seen by AFP, was issued as polls closed in the key presidential run-off.
The document amends a constitutional declaration issued in March 2011, after Egypt's uprising. It also states that no vote to elect a new parliament can be held until a permanent constitution is written.
And it effectively grants the Supreme Council of the Armed Forces in control of the country veto rights over the text of any new constitution.
Egypt's Islamist-dominated parliament was elected in a drawn-out process between November 2011 and January 2012. SCAF handed power to the new parliament in January.
But on Thursday, Egypt's constitutional court effectively annulled the body, ruling that a third of its members had been elected illegally, and the military subsequently informed the body that it considered it dissolved.
Before the court ruling, the parliament had selected a constituent assembly, replacing an earlier group that had been disbanded amid accusations of an Islamist monopoly.
It was not immediately clear if that replacement assembly would be allowed to proceed with its work, or be replaced with a new grouping.
The Freedom and Justice Party, the political arm of the Muslim Brotherhood, which dominated the dissolved parliament, has already rejected any attempt by the military to retake legislative power.
And earlier on Sunday, parliament speaker and FJP member Saad al-Katatni warned against the issuing of an amended constitutional document that sought to strip the parliament of power.