* Police say investigation not complete
* U.S. wants immediate release of the accused
* Islamist groups warn against release
(Updates with protest outside U.S. consulate)
By Mubashir Bokhari
LAHORE, Pakistan, Feb 3 (Reuters) - An American who killed two Pakistani men last week will be held for eight more days to allow for more investigation, a prosecutor said on Thursday, despite U.S. insistence the man has diplomatic immunity.
The case of Raymond Davis has become the latest test of ties between the two countries with anti-U.S. Islamist groups demanding the Pakistani government resists U.S. calls to free him.
The United States says Davis is a diplomat and has called for his immediate release. He was arrested a week ago after shooting dead two men in the city of Lahore in what Davis says was an act of self-defence during an attempted robbery.
The Lahore High Court on Tuesday barred the government from handing him over to Washington, saying it would decide whether he had diplomatic immunity or not.
Amid tight security, police brought Davis in an armoured car to appear before a magistrate in Lahore on Thursday. Journalists were barred from the proceedings.
"The police officials told the court that investigations have not yet been completed. The judge extended the remand(detention) for eight more days," Abdul Samad, a deputy prosecutor general at the high court told Reuters.
Davis told the court that he opened fire on the two motorcyclists in self-defence, fearing that they were about to rob him. The two men later died in the hospital.
Hundreds of supporters and some relatives of the two men, as well as those of a man who police said was run down and killed when U.S. personnel in a consulate vehicle apparently tried to rescue Davis, held a protest rally later on Thursday.
The protesters marched to the U.S. consulate and burned U.S. flags. They said the government should not hand Davis over to U.S. Authorities, witnesses said.
Pakistan is a crucial ally to the United States in its efforts to stabilise Afghanistan and combat Islamist militancy, but anti-American sentiments run high in the predominantly Muslim country.
The government of President Asif Ali Zardari, already weakened by a host of problems from political wrangling, Islamist militancy and a fragile economy, has to act cautiously as the case is politically explosive.
After first identifying the man as a staff member of the U.S. consulate in Lahore, the U.S. embassy on Saturday described him as a diplomat and said he had been unlawfully detained.
Arresting a diplomat is a violation of international norms and the Vienna Conventions, it said.
Interior Minister Rehman Malik told the Senate on Wednesday that Davis held a diplomatic passport but maintained that his case would be settled by a court.
A Western diplomat said it was possible that Malik's comments were laying the groundwork for Davis' eventual release under laws governing diplomatic immunity. (Additional reporting by Chris Allbritton; Writing by Zeeshan Haider; Editing by Rebecca Conway and Sanjeev Miglani) (For more Reuters coverage of Afghanistan and Pakistan, see:http://www.reuters.com/places/pakistan. (If you have a query or comment about this story, send ane-mail to news.feedback.asia@thomsonreuters.com)
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