Dushanbe, Tajikistan, July 31, 2018 (AFP)

Police in Tajikistan Tuesday linked an attack claimed by the Islamic State group that killed four tourists including two Americans to a banned Islamist opposition group and Iran.

The victims -- two Americans and a Swiss and Dutch citizen -- were struck by a car and attacked on Sunday on a popular cycling route in the impoverished Central Asian country.

Two citizens of Switzerland and the Netherlands were also injured in the attack in the Danghara district, about 100 kilometres (62 miles) from the capital Dushanbe. A French citizen survived unscathed.

In a statement on Monday, the Islamic State group claimed a "detachment from the soldiers of the Caliphate" had carried out the attack against "citizens of Crusader coalition countries."

A Tajik police statement on Tuesday ignored the IS claim and said the chief detained suspect was a member of a banned Islamist opposition party and had undergone "military sabotage" training in Iran.

The suspected attack leader, Hussein Abdusamadov, 33, was an "active member" of the Islamic Renaissance Party of Tajikistan, which was banned by the government in 2015, police said.

Police said the suspect also testified that he had travelled four times to Iran, a country with which Tajikistan has poor relations, "where he received an ideological education and underwent military sabotage training."

The statement made no explicit reference to terrorism but said "the crime was committed with the goal of making an attempt on state and public security (and) destabilising public order."

The state prosecutor has opened a murder investigation and police said they have killed at least four people suspected of involvement after they resisted arrest and detained a further four suspects.

The attack on the tourists cycling a popular route was initially reported as a hit-and-run, but Tajikistan's interior minister Ramazon Hamro Rahimzoda said on Monday that the group had been armed with "knives and firearms."

At least one of the three tourists who survived the attack is being treated for stab wounds in hospital, the minister told a press conference.

- Tense ties -

The police account is likely to generate scepticism in the context of the two countries' tense bilateral relationship and after Tajikistan's crackdown on the IRPT was criticised by the United States and several rights groups.

While majority-Muslim Iran and Tajikistan share a Persian cultural and linguistic heritage, ties have been bedevilled by tensions.

Although Muslims in Tajikistan overwhelmingly adhere to the Sunni Islam, Shia Islam dominates in Iran, limiting religious ties between the two countries.

In 2016, a Tajik court gave life sentences to key figures in the IRPT, a group the government has accused of plotting to overthrow the government.

A US Embassy statement at the time raised concerns the members had not been granted a fair trial.

Some members of the IRPT had fought government forces in the civil war in Tajikistan that lasted from 1992 to 1997.

The party's subsequent participation in domestic politics was widely viewed as a positive legacy of the peace process.

Tajik authorities have declared 2018 "a year of tourism" in the former Soviet republic.

In June, President Emomali Rakhmon said that state officials found to be soliciting bribes from tourists would be deemed "traitors" and fired from their positions.