The tourists, from the United States, Switzerland and the Netherlands, were killed in the Central Asian country on Sunday, the authorities said.
The U.S. Embassy confirmed the attack with multiple sources and said that Tajikistan's ministry of internal affairs had detained one suspect and killed at least three others. Three other suspects are still at large.
Dutch newspaper the Telegraaf reported that one of the deceased tourists as a 56-year-old man who had been cycling from Thailand to Iran with his 58-year-old girlfriend.
Two of the victims were American, the U.S. Embassy in Tajikistan said.
In a Tweet on Monday, the group said that "soldiers of the Caliphate" launched the attack on "citizens of Crusader coalition countries", running them over and then using knives, according to ABC's translation.More news: Demi Lovato 911 call: 'No sirens please'
A Belgian cyclist who said he arrived at the scene after the attack told Flemish broadcaster VRT that he saw "several cyclists on the ground". Officials said they died when they were run down by a auto Sunday and attacked with knives and guns.
Ramazon Rakhimzoda said: "During active search operations, the auto that ran into the group of tourists was found". The stab victim, whose nationality was not given, was in a stable condition.
Tajikistan declared 2018 a "year of tourism", ABC noted, adding officials have been cautious about labeling the incident as terrorist activity.
Tajikistan brushed off the earlier claim of responsibility by the IS group, saying the leader of the attackers was Hussein Abdusamadov, an "active member" of the Islamic Renaissance Party of Tajikistan (IRPT).
Tajikistan's President Emomali Rakhmon sent notes of condolence to the US, Switzerland and the Netherlands over the deaths and called for increased security throughout the country at a special meeting on Monday with the country's law enforcement chiefs.