UPDATE 2-Malaysia asks Interpol help to find missing detective

(Updates with Anwar's speech at protest rally; fresh quotes)

By Soo Ai Peng and Niluksi Koswanage

KUALA LUMPUR, July 6 (Reuters) - 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.