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 from Islamist militants said they 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 US embassy said its diplomats were instructed not to go outside overnight following the attack and warned of possible attacks on US facilities, citizens and interests.