KUALA LUMPUR (Reuters (LSE: TRIL.L - news) ) - Malaysian police on Sunday issued an international alert for a missing private eye after he made, and abruptly retracted, allegations about the deputy prime minister's links to a high-profile murder case.

The detective, Balasubramaniam Perumal, disappeared along with his wife and three children on Friday after retracting an allegation that Deputy Prime Minister Najib Razak had sexual relations with the murder victim.

The allegation was the latest twist in a political melodrama -- featuring allegations of sex, murder and lies -- that has gripped the nation and unnerved foreign investors since a March 8 general election handed a resurgent opposition led by former deputy premier Anwar Ibrahim unprecedented gains.

Anwar, mired in a sodomy allegation that rocked the nation, told a 20,000-strong crowd at a rally protesting fuel price hikes that he was willing to debate the issue with the prime minister or his deputy.

"It is better if I debate with the PM," said Anwar, who was earlier scheduled to hold a televised debate with a junior minister on July 15 on the subject.

Thousands of people, defying police orders to shun the rally, had gathered at a soccer stadium outside Kuala Lumpur. A police helicopter hovered above the stadium.

"Azizah, Kit Siang and other MPs will stand in parliament tomorrow to demand a reduction in fuel prices. They will convey the wishes of the people," he told the crowd. He was referring to opposition leaders Wan Azizah Wan Ismail and Lim Kit Siang.

Police have declared the event an illegal gathering but are allowing it to proceed as long as the rally is confined to the stadium grounds, officials said.

Anwar told the crowd that he would press ahead until his opposition alliance ousts the National Front coalition that has ruled the country since independence from Britain in 1957.

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The Mongolian woman, Altantuya Shaariibu, 28, was shot in the head twice before her body was blown up with C4 explosives in October 2006. Najib's political adviser, Abdul Razak Baginda, and two policemen are on trial for the murder.

Najib has repeatedly denied he ever had a sexual relationship with the Mongolian, or had conspired to cover up her murder, allegations made on Thursday by Balasubramaniam, who was working for Abdul Razak at the time of the killing.

National Police Criminal Investigation Department (CID) chief Bakri Zinin said on Sunday police in Malaysia and neighbouring countries had been put on alert to find Balasubramaniam, and Interpol had been informed.

"I give a guarantee of his safety, if he comes to meet us, and he is free to bring a lawyer," Bakri told a news conference.

Najib and Anwar are competing to become Malaysia's next prime minister with control over a political patronage system that dominates the economy. Both are battling accusations that could ruin their political careers.

The rally, which ended at almost 11 p.m. ( 4 p.m. British time), had a convivial atmosphere with most people wearing red T-shirts, the colour of the protest movement.

The crowd, who chanted "Bring Down Oil Prices", also asked Prime Minister Abdullah Ahmad Badawi to step down.

"I love Anwar ... he is innocent and he is our hope," said 35-year-old computer executive Mohamad Amran Amiruddin.

"Oil has gone up. Goods have gone up. People are left with less money," said Faridah Jantan, 48, mother of five children. "This weekend we will take up the fight. We want a more democratic nation."

Abdullah's government raised petrol prices 41 percent last month, adding to its unpopularity after the opposition won power in five of Malaysia's states and came within 30 seats of taking over the 222-member national parliament.

Anwar said he was on the verge of winning that majority in parliament by wooing defectors from the ruling coalition when a 23-year-old aide suddenly accused him of sodomy, a crime punishable by up to 20 years in prison.

Anwar said on Thursday the sodomy allegations surfaced because leading government figures feared he would use the detective's statements in the Altantuya case in his drive to lead the opposition to power for the first time in Malaysia.

(Writing by Bill Tarrant and Jalil Hamid; Editing by Dominic Evans)