CAIRO (Reuters) - A group of high profile liberal and leftwing politicians in Egypt has said it will quit the assembly charged with drafting the country's new constitution within a week unless its concerns over Islamist-influenced content in the document are addressed.

The constitution - which is being drawn up by a 100-member assembly - is meant to be the centerpiece of a new democratic Egypt after veteran autocrat Hosni Mubarak was ousted last year and its successful drafting is being seen as a litmus test for its new Islamist rulers including President Mohamed Mursi.

Egypt can't hold an election to replace a parliament that a court declared void in June without the constitution, and until it does Mursi will continue to hold lawmaking power, an uneasy arrangement that erodes the credibility of his government.

But during a closed door meeting held late on Tuesday but that was only made public on Thursday three former presidential candidates and several leaders of the country's main non-Islamist parties said they were ready to quit the assembly or encourage their supporters to do so.

If they make good on their threat, a new parliamentary election could be delayed.

Arguing that Islamist influence meant the constitution risked ending up as a document that curbed freedom, they said they would resign in one week and take to the streets unless their concerns were addressed.

"This is a constitution that brings Egypt backwards not forward," said Ahmed al-Boraie, a former labor minister who hosted the meeting.

"We are consulting with political powers that have the same demands, if the assembly doesn't respond they will have to quit," he said.

In particular, liberals oppose a proposal that would give the seat of Sunni learning, Al-Azhar, authority similar to that of a supreme court by making it the arbiter of whether a law conforms with the principles of sharia law.

They are also unhappy with clauses that would allow journalists embroiled in publishing lawsuits to be jailed and other proposed measures which they say will curb freedom of belief and expression.

"TOO MANY ISLAMISTS"

Mursi, propelled to power by the Muslim Brotherhood, has praised the assembly, and has said he doesn't understand those who quit.

Some liberals committed to a more secular state have already boycotted the assembly and are challenging it in court, saying it includes too many Islamists. They say the Islamists want to turn Egypt into an Iran-style theocracy, a claim Islamists deny.

A court will consider a legal challenge against the assembly, which is made up of thinkers, scholars, professionals and political and religious leaders, on October 2.

Islamist politicians make up almost half the assembly while the other half includes many Islamist-sympathizers. A court dissolved a previous assembly for being dominated by Islamists and for failing to fairly represent Egypt's diverse society.

The clauses the liberals want dropped are being championed by ultraconservative Salafis. Other Islamists, such as members of the Brotherhood and its Freedom and Justice Party (FJP), are pressing for a consensus to be reached in order to keep the assembly working.

"We are very committed that everyone work together," said Farid Ismail, an FJP assembly member. "This isn't the FJP or Salafis assembly, it concerns all Egyptians."

Manal al-Teiby, a liberal member of the assembly, quit earlier this week objecting to the way it was operating. The assembly's speaker, Hossam al-Gheriany, who is also head of Egypt's Supreme Judicial Council and is seen as an independent, criticized her resignation, saying her accusations were false.

"There is a very severe attack" on the assembly, he said.

Analysts expect the new document to have a more Islamic flavor than its predecessor, including clauses prohibiting criticism of God and establishing an institution to collect zakat, or charitable donations for the poor. An existing clause banning parties based on religion is also likely to be dropped.

Amr Hamzawy, a prominent liberal politician and ex-MP, demanded that liberals lobby international parliamentarians.

"These circles, especially the European Parliament and the American Congress, can pressure their governments to convey a message to Mursi and Islamist parties that financial and economic aid are linked to building a democracy," he wrote on Wednesday in the al-Watan privately-owned newspaper.

(Reporting By Tamim Elyan; Editing by Andrew Osborn)