DHAKA (Reuters) - The United States and Britain have restricted movements of their diplomats in Bangladesh and cited "reliable" information that more Westerners will be targeted after gunmen believed to be Islamist militants killed an Italian aid worker in Dhaka.

Aid worker Cesare Tavella was shot dead by gunmen on a motorbike on Monday evening in Dhaka's diplomatic zone, the latest sign of growing extremism on the city's streets after four liberal bloggers were hacked to death.

The U.S. embassy said its diplomats were instructed not to go outside overnight following the attack and warned of possible attacks on U.S. facilities, citizens and interests.

"In light of the increased threat, U.S. citizens should consider limiting their attendance at events where foreigners may gather, including events at international hotels," the U.S. embassy said in a statement issued late on Monday.

Britain told embassy officials to stay away from events where westerners may gather and warned of possible attacks in "late September."

The motive behind the shooting of Tavella was unknown, acting inspector general of police Mokhlesur Rahman said.

"But based on our experience, we can say it is a pre-planned murder," he told reporters after visiting the crime scene in the upscale Gulshan neighborhood, home to several embassies.

An online statement in the name of the hardline Islamist group Islamic State claimed responsibility for the attack on Tavella. Police said they were not aware of the claim, which could not be independently verified.

Lat week, the Australian cricket team delayed its planned departure to Bangladesh after being warned there was a potential security risk from militants. The touring side were due to fly from Sydney on Monday morning for the three-week tour.

"There is reliable information to suggest that militants may be planning to target Australian interests in Bangladesh. Australian officials in Bangladesh have been advised to limit their movements in public places," an advisory said.

The government in Bangladesh has been tackling Islamist groups which aim to make the South Asian nation of 160 million people a sharia-based Islamic state.

Four online critics of religious militancy, including a U.S. citizen of Bangladeshi origin, have been hacked to death in the Muslim-majority nation this year.