DHAKA, Sept 21 (Reuters) - A Bangladesh court refused bail on Sunday to 10 suspected members of the radical Islamist group Hizb ut-Tahrir, which had threatened to bomb key installations if they were not released.

Police said militants had said in faxed messages that they would launch bomb and grenade attacks unless the detainees were freed without delay.

One fax was received at the police commissioner's office in the western Rajshahi city on Saturday evening. Similar messages were sent to several police headquarters on Sept. 4, police said.

Police detained 10 members of the banned group, including three university teachers, when they tried to hold a news conference at the Rajshahi press club on Thursday.

Police said they were held on suspicion of plotting subversive acts against the country. The court refused to grant them bail.

Rajshahi, 350 km (230 miles) from the capital Dhaka, is considered a breeding ground of Islamist militants who have carried out a campaign of violence across the country.

"We have issued a high security alert in Rajshahi and other main cities," a Rajshahi police officer said.

Government officials say the militants are seeking to impose sharia-based Islamic law in Bangladesh, a Muslim majority nation which follows a secular constitution.

Members of outlawed Islamic groups Jammat-ul-Mujahideen and Jagrata Muslim Janata rocked the country in August 2005 by exploding about 500 small bombs in a single day, killing six people and wounding dozens.

They carried out more attacks in the following months, killing at least 25 people including lawyers, judges and police.

Security forces arrested hundreds of militants from the two groups. Six of their top leaders were captured, tried and hanged in March 2006.

But police say remnants of the two groups, along with militants from other organisations like Hizb ut-Tahrir are regrouping and may launch fresh attacks ahead of a national election due on December 18. (Reporting by Ruma Paul; Writing by Anis Ahmed; Editing by Dominic Evans)

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