CAIRO — Egypt's prime minister-designate vowed Friday before thousands of demonstrators at a central Cairo square to do everything he could to meet their demands for political change and pleaded with them to turn their attention to "rebuilding" the country.

Meanwhile, the Supreme Armed Forces Council that took control of the country from ousted President Hosni Mubarak said a referendum on constitutional changes to allow for competitive parliamentary and presidential elections will be held on March 19.

The new prime minister, Essam Sharaf, was picked by Egypt's military rulers on Thursday to replace Ahmed Shafiq. Shafiq was the last premier to be named by Mubarak, and his resignation was among the major opposition demands.

A former transport minister, Sharaf endeared himself to the protesters when he joined the demonstrations that forced Mubarak to resign. He made his address Friday at Tahrir Square, the protests' epicenter.

"I draw will and determination from here," he told the estimated 10,000 demonstrators. "I will do my utmost to realize your demands," he said, pledging to step down if he fails.

Sharaf, a U.S.-educated civil engineer, served in the Cabinet for 18 months between 2004 and 2005.

His appearance at the square on Friday — he was carried on the shoulders of demonstrators to and from the podium — was the latest evidence of the power retained by youth groups nearly a month after they ousted Mubarak. Sharaf's government will serve in a caretaker capacity until elections are held.

However, Sharaf declined to take an oath of office before the demonstrators as they demanded and left the square amid chants of "Swear! Swear!"

The protesters had planned the Friday rally to press for Shafiq's resignation. When he stepped down a day earlier, they said they would go ahead with their gathering to celebrate what they consider the latest victory for the 18-day popular uprising that forced out Mubarak on Feb. 11.

They also chanted slogans against Moammar Gadhafi, and one protester held a picture of the Libyan leader crossed out with the word "mad" plastered over it. Gadhafi is trying to hold on to power amid an armed rebellion that took shape after he violently cracked down on anti-government protesters.

Besides Shafiq's resignation, the revolt's leaders want Mubarak's National Democratic Party dissolved along with the hated State Security Agency blamed for some of the worst human rights violations during Mubarak's rule. Other demands include the prosecution of security officials behind the deaths of protesters and the release of political prisoners.

"I am here because I get my legitimacy from you," Sharaf, in a gray business suit but no tie, told the demonstrators. He called on the protesters to turn their attention to "rebuilding Egypt."

"I pray to God that I see an Egypt where free opinions are voiced outside (prison) cells and security agencies are in the service of the nation."

Sharaf is forming a new Cabinet. He is faced with the daunting task of restoring a sense of normalcy in the country, where police forces have largely disappeared from the streets and there is growing sense of insecurity. The stock market has been closed for over a month, and since Mubarak left there have been countless labor and other strikes. Eleven universities were set to reopen on Saturday.

The constitutional changes to be voted on affect 10 articles of the currently suspended charter. They open presidential elections to competition and impose a two-term limit on future presidents — a dramatic shift from a system that allowed Mubarak to rule for three decades.

The proposals address a number of the demands of the reform movement. But many say the changes don't go far enough and debate is still under way over which election should come first.

Since it took charge of managing Egypt's affairs, the military has promised to hand power to a new government and elected president within six months. It disbanded both houses of parliament and promised to repeal the emergency laws, though only when conditions permit.

Despite the military's swift moves, there is still much unrest throughout the country.

On Friday, protesters in the northern Sinai took to the streets demanding the release of scores of detainees and prisoners, saying that many are being held without charge or are still incarcerated despite finishing their sentence.

Thousands marched in the city of El-Arish and other smaller towns. A few hundred blocked the road to the compound of the Multinational Forces and Observation — an independent force created by Egypt and Israel to monitor their border in the Sinai after their 1979 peace deal.

Associated Press writer Ashraf Sweilam contributed to this report from El-Arish, Egypt.