Japanese doctor Kursio Martia (centre) and the Japanese embassy's chief security officer walk with Bangladesh police as they inspect the body of Japanese citizen Kunio Hoshi  in Rangpur on Sunday.

AFP/Dhaka

Bangladesh Prime Minister Sheikh Hasina on Sunday dismissed the Islamic State's claim to have killed two foreigners, saying police still had no evidence to confirm the jihadist group was behind the murders.

Her remarks came a day after 66-year-old Japanese citizen Hoshi Kunio was shot dead in northern Bangladesh, the second foreigner to be murdered in the South Asian nation in less than a week.

A 50-year-old Italian, Cesare Tavella, was shot dead last week near Dhaka's diplomatic zone in another attack also claimed by IS.

"We have still not found any involvement (of IS). We have to investigate," Hasina told reporters.

"We've got no clues. If someone claims responsibility, why should we have to accept it?" she added.

"Until we find out the link through investigation, I don't think there is any reason for us to accept it."

Italian aid worker Tavella was shot three times on September 28 by attackers who fled on a motorcycle - an attack the Bangladesh government described as an "isolated incident" in an attempt to calm security fears.

Kunio was riding in a rickshaw when he was shot dead by three unidentified attackers riding a motorbike in the town of Kaunia in Rangpur district.

Home Minister Asaduzzaman Khan Kamal has rejected any IS presence in the country but said the two killings appeared to be linked.  

"I can again say boldly that there is no existence of IS in Bangladesh," he said on Sunday, adding such murders were "an attempt to create instability in the country".

Bangladesh prides itself on being a mainly moderate Muslim country. But the gruesome killings of a series of atheist bloggers this year have rocked the nation and sparked a crackdown on local hardline Islamist groups.

After the murder of the Italian, international schools closed temporarily and Western embassies restricted their diplomats' movements, while Australia's cricket team cancelled a planned tour due to security concerns.

"Extra forces have been deployed at foreign diplomats and citizens' homes and workplaces across the country," Muntasirul Islam, a deputy commissioner of the Dhaka Metropolitan Police, told Reuters.

Dhaka police arrested two suspected recruiters for the hardline Islamist group over the past year.

Attacks warned

On Saturday, Islamic State warned of more attacks.

"There will continue to be a series of ongoing security operations against nationals of crusader coalition countries, they will not have safety or a livelihood in Muslim lands," the group tweeted.

After Tavella's killing in the Gulshan neighbourhood, home to several embassies, concerns that foreigners might be targeted prompted Western embassies to curtail the movements of diplomats in Bangladesh.

Australia postponed their tour of Bangladesh, saying on Thursday they were advised against going ahead with a two-test series that could expose their cricketers to potential militant attacks in the country.

Police are interrogating four people for clues to Hoshi's killing, but no arrests have been made over Tavella's murder.

The violence could pose a fresh threat to Bangladesh's  $25bn garment export industry, the economic lifeblood of the country of 160mn people.

Western buyers had begun to cancel visits after Tavella's shooting, said Shahidullah Azim, a garment exporter.

"One of my American buyers also cancelled his Dhaka visit during peak time, when buyers are supposed to place more orders," he told Reuters.

"The killing of a Japanese citizen within a week has created more panic among foreign buyers."

The garment industry, which supplies Western brands such as Wal-Mart, JC Penney and H&M, has already been in the spotlight over several fatal accidents, such as the 2013 collapse of a building that had factories which killed more than 1,130 people.