CAIRO, Egypt (CBS) -- Votes are still being counted in Egypt's Presidential run-off election, but the Muslim Brotherhood is already claiming victory. Supporters are cheering what they hope will be the end of six decades of military rule.

Supporters of the Muslim Brotherhood party jammed the streets in Cairo to declare victory. Islamist candidate Mohammed Morsy says he was won the Presidency.

He promised a new path to a peaceful Egypt. But his rival, former Prime Minister Ahmed Shafik refused to concede saying he was beating Morsy "beyond all doubt."

It was the first free vote since the ouster of Dictator Hosni Mubarak 16 months ago. One man says power has been transferred to civilians for the first time in Egyptian history.

Egypt's Army will reportedly hand over control to the newly elected President at the end of the month. But just before Sunday's election, it tightened its grip on power.

The military issued a declaration stripping the new President of any authority over the armed forces. One man says "The military has been trying to steal the revolution, but they cannot take power from our President!"

But until final results are announced there is no official President. The outcome of the race is expected to be known on Thursday.