Three more, from Switzerland, the Netherlands and France, were injured - one of them also had a stab wound.
Three other cyclists in the group, including a Swiss woman, sustained injuries and sought medical help, according to Tajik and Swiss officials.
The US embassy in Dushanbe confirmed two of the fatalities were US citizens, but did not provide further details "due to privacy concerns".
The tourists, from the US, Switzerland and the Netherlands, were killed on Sunday.
Later, officials said three of the four people believed to be in the auto at the time of the collision were tracked down to a village called Torbulok and that two of them were killed while resisting detention.
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The men in the vehicle then attacked the survivors with knives and guns, the interior ministry said.
The cyclists were travelling on a road that adjoins the famous Pamir Highway, a Soviet-era road surrounded by stunning mountain scenery.
'We are considering all possibilities, ' Rahimzoda said of the criminal investigation.
"If it is established that this was a terrorist attack, it will be noted in future travel advice for Tajikistan", the ministry said in a statement.
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A French diplomatic source told AFP that the country's embassy in Tajikistan was "engaged in facilitating the return" of the French survivor of the attack.
Tajik President Emomali Rahmon extended condolences to U.S. President Donald Trump, Swiss President Alain Berset, and King of the Netherlands Willem-Alexander.
A State Department official said it was not yet identifying the victims, and referred questions on the incident to local authorities.
Visitor numbers had quadrupled in the first five months of 2018 compared the same period a year ago, he said.
Tajikistan is one of the poorest former Soviet republics and has struggled with poverty and instability since its independence in 1991.
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