* Early indications suggest measure will pass
* Constitution backed by 57 percent in first round vote
* Rights groups report some irregularities
By Yasmine Saleh and Edmund Blair
CAIRO, Dec 23 (Reuters) - Early indications suggested Egyptians approved an Islamist-drafted constitution in Saturday's second-round referendum despite opposition criticism of the measure as divisive.
As counting began, an official from the Muslim Brotherhood's political party, which backs President Mohamed Mursi, said a sample of a few hundred thousand votes had "yes" in the lead.
An official from the opposition National Salvation Front said their early exit polls showed the constitution passing.
Last week's first round returned 57 percent in favour of the constitution, according to unofficial data. The vote was split over two days as many judges refused to supervise the ballot.
The referendum committee may not declare official results for the two rounds until Monday, after hearing appeals.
Islamist backers of Mursi say the constitution is vital to move to democracy, nearly two years after an Arab Spring revolt overthrew authoritarian ruler Hosni Mubarak. It will provide stability for a weak economy, they say.
But the opposition accuses Mursi of pushing through a text that favours Islamists and ignores the rights of Christians, who make up about 10 percent of the population, as well as women.
"I'm voting 'no' because Egypt can't be ruled by one faction," said Karim Nahas, 35, a stockbroker, heading to a polling station in Giza, in greater Cairo.
At another polling station, some voters said they were more interested in ending Egypt's long period of political instability than in the Islamist aspects of the charter.
"We have to extend our hands to Mursi to help fix the country," said Hisham Kamal, an accountant.
VICE PRESIDENT ANNOUNCES RESIGNATION
Hours before polls closed, Vice President Mahmoud Mekky announced his resignation. He said he wanted to quit last month but stayed on to help Mursi tackle a crisis that blew up when the Islamist leader assumed wide powers.
Mekky, a prominent judge who said he was uncomfortable in politics, disclosed earlier he had not been informed of Mursi's power grab. The timing of his resignation appeared linked to the lack of a vice-presidential post under the draft constitution.
Rights groups reported alleged law violations during voting. They said some polling stations opened late, that Islamists illegally campaigned at some of them, and complained of voter registration irregularities, including listing of a dead person.
The new basic law sets a limit of two four-year presidential terms. It says sharia law principles remain the main source of legislation but adds an article to explain this further. It also says Islamic authorities will be consulted on sharia - a source of concern to Christians and other non-Muslims.
If the constitution passes, there will be parliamentary elections in about two months.
After the first round of voting, the opposition said alleged abuses meant the first stage of the referendum should be re-run.
But the committee overseeing the two-stage vote said its investigations showed no major irregularities in voting on Dec. 15, which covered about half of Egypt's 51 million voters. About 25 million were eligible to vote in the second round.
If the charter is approved, the opposition says it is a recipe for trouble since it will not have received sufficiently broad backing and that it will not have been a fair vote.
"I see more unrest," said Ahmed Said, head of the liberal Free Egyptians Party and a member of the National Salvation Front, an opposition coalition formed after Mursi expanded his powers on Nov. 22 and then pushed the constitution to a vote.
Protesters accused the president of acting like a pharaoh, and he was forced to issue a second decree two weeks ago that amended a provision putting his decisions above legal challenge.
Said cited "serious violations" on the first day of voting, and said anger against Mursi was growing. "People are not going to accept the way they are dealing with the situation."
At least eight people were killed in protests outside the presidential palace in Cairo this month. Islamists and rivals hurled stones at each other on Friday in Alexandria, the second-biggest city. Two buses were torched.
Late on Saturday, Mursi announced the names of 90 new members he had appointed to the upper house of parliament, state media reported, and a presidential official said the list was mainly liberals and other non-Islamists.
Mursi's main opponents from liberal, socialist and other parties said they had refused to take any seats.
Two-thirds of the 270-member upper house were elected in a vote early this year, with one third appointed by the president. Mursi, elected in June, had not named them till now. Mursi's Islamist party and its allies dominate the assembly.