CAIRO, Nov 9 (Reuters) - Thousands of Islamists rallied in Cairo on Friday to demand immediate introduction of sharia and called on President Mohamed Mursi to resist opposition to Islamic law.

Islamists, Liberals and non-Islamists have locked horns over what civic freedoms women, Christians and minority groups will enjoy under a new constitution being drafted by an Islamist-dominated panel.

The constitution is supposed to become the cornerstone of democratic transition after the uprising that ousted Hosni Mubarak last year. Without it, the country cannot hold elections to replace a parliament that a court declared void in June.

The Islamist camp is divided. Islamists on the panel are aiming to reach consensus over the constitution, but Friday's rally brought together groups with little representation on the body - including the Salafist Front, its political arm the People Party, the Gamaa Islamiya and its Building and Development Party.

Many waved banners with the words: "God's law is our constitution". The Saudi Arabian flag was seen flying over a sea of Islamist protesters. The Egyptian flag was missing.

"The people demand God's law implemented," chanted thousands of demonstrators.

Asked what implementing sharia meant for them, many said it involved eradication of corruption and loose sexual behaviour, modesty in men and women's dress, and improved living conditions.

Mursi's ruling Muslim Brotherhood, which says it favours only a gradual introduction of sharia, and the ultraconservative al-Nour Party refrained from participating. Both are well represented in the 100-strong constitutional panel.

"We are not coming out to oppose the assembly but to tell it and President Mursi that sharia must be implemented immediately not later. I voted for Mursi to implement God's sharia," said Hassan Abdel Maqsood from the city of Minya.

Another protester demanded a more unequivocal reference to sharia in the constitution. The current draft talks of implementing "the principles of sharia".

"We do not want the misleading word 'principles'. The assembly should not listen to the secularists and the small elite. These people have other motives and want the country to live in chaos," said Mohamed Salama of the Gamaa Islamiya.

Cairo sees demonstrations almost every Friday, the Muslim day of prayer, by a range of groups in the aftermath of the revolution that overthrew strongman Hosni Mubarak last year.

MURSI UNDER PRESSURE FROM BOTH SIDES

Pressure is mounting on the constitutional panel to finish its job by December 12. Should it fail, Mursi may have to use his legislative powers to find a way out.

Analysts say Mursi is torn between pleasing Islamist hardliners who voted him into power and gaining national and international legitimacy.

"President Mursi is in a bind and must please disparate groups," Ammar Ali Hassan, Islamist thinker and analyst, told Reuters.

"He cannot do it without changing his discourse. He tells liberals and the international audience that Egypt is a moderate, modern and civil state. But to his Islamist backers across the country he must say that sharia will be implemented."

Struggling to overcome disputes, Mursi has met party leaders and politicians from both Islamist and liberal camps to try to broker consensus over the constitution.

The Brotherhood's ruling Freedom and Justice Party had no majority in the last parliament without the backing of Salafist hardliners, added Hassan.

Mursi would lose his legitimacy as leader should Salafists vote "no" in a referendum for national approval to be held on the constitution once it is finished, said Hassan.

Members of the Brotherhood leadership have complained that rifts among Islamists could cost them politically ahead parlimentary elections. No date has been set yet for the vote.

Egyptians who oppose the Islamists say the country's civil laws already implement sharia.

"Look at marriage, divorce and inheritance laws. All of the country's civil laws are compatible with sharia. The protesters today have confined sharia to the application of penal (criminal) law," said Achraf Chazly, a 35-year-old lawyer. (Additional reporting by Omar Fahmy, Shaimaa Fayed and Reuters TV; Writing by Marwa Awad; Editing by Andrew Roche)