* Interim president says vote is the correct start
* Muslim Brotherhood yet to announce its position from vote (Recasts with president's announcement, adds details)
By Omar Fahmy
CAIRO, Dec 14 (Reuters) - Egyptians will vote on a new constitution on Jan. 14 and 15, pushing on with the army-backed government's plan for transition back to democracy after its overthrow of elected Islamist President Mohamed Mursi.
The new document is designed to replace one passed by Mursi, deposed by the army in July after mass protests against his rule. It should pave the way for new parliamentary and presidential elections to take place next year.
It is not clear how Mursi's Muslim Brotherhood, outlawed by a court in September and under pressure from a wide-ranging security crackdown on leaders and activists, will react.
"The document in our hands today should bring pride to every Egyptian," Mansour said in a televised speech. "It is the correct starting point to build the state's democratic and modern institutes that we all look forward to."
A 50-member assembly appointed by Mansour finished the new draft earlier this month, removing Islamist-inspired provisions from the constitution that was approved in a referendum last year while Mursi was still in office.
Among other changes, the new draft deepens the autonomy of the already powerful military while offering more room on freedoms and women's rights and allowing the authorities to switch the order of elections expected next year. The initial plan unveiled in July required parliamentary elections to be held first, but the new constitution could allow presidential elections first.
The new draft also restricts the formation of religious political parties and allows the armed forces - not the president - to pick the minister of defence for two full presidential terms.
About 50 million Egyptians of the population of 85 million have the right to vote in the constitutional referendum and many of those interviewed by Reuters on the streets of Cairo on Saturday wanted to get on with the transition.
"I want to say yes in the vote so that the country gets back on track," said Ahmed Mahmoud, a 27-year-old banker.
The committee was dominated by liberals and leftists and chaired by Amr Moussa, a former Arab League secretary general and former candidate for the presidency. It included two Islamists, who had both backed the army's move against Mursi.
"It is your time to impress the world one more time by going to vote and express your free will," Mansour said, speaking in front of a crowd of ministers, religious clerics and members of the committee who drafted the document.
Islamists won all the elections organised after the fall of autocratic President Hosni Mubarak in 2011. But their popularity was harmed by a year of Mursi rule that failed to enact any reform.
Mansour's army-backed government has cracked down hard on the Islamists, killing hundreds and jailing thousands.
The Muslim Brotherhood, the country's most organised movement, does not recongnise the current regime and says it is illegitimate and brought by a military coup.
"We are confronting callers for destruction," Mansour said speaking to his people about the Brotherhood.
"So let's begin rebuilding this great state that had just started to regain its dignity and which has wealth and experience that could allow it in the near future."
The Brotherhood has yet to announce whether it will call for a no vote or boycott the entire process. Brotherhood officials, most of whom are either on the run or outside Egypt could not be immediately reached for comment.
Some liberal politicians had called on the group to participate in the vote to prove its popularity.
"Instead of conducting daily violent protests, they could use this chance to prove their presence through ballot boxes and put down the constitution," said Khaled Dawoud, spokesman of the Dostour liberal party.
Mansour also had a message to the Brotherhood in his speech.
"I don't wish to end this speech without talking to those who had opposing views in the past period: Be brave and stop your stubbornness and join the national crowd." (Additional reporting and writing by Yasmine Saleh; Editing by Patrick Graham)