Russia's FSB Security Service said Saturday it has arrested the man who set off a homemade bomb in a St. Petersburg supermarket.
Eight people remain hospitalized after a device exploded Wednesday in a storage area for customers' bags.
Putin said following the explosion: "I have instructed the director of the Federal Security Service to act within the framework of the law during detention (of suspected terrorists)".
"The attack that targeted a shopping centre in Saint Petersburg on Wednesday was carried out by an Islamic State-linked group", IS said in a statement via its propaganda agency Amaq.
The Islamic State group claimed responsibility on Friday for the bomb attack days earlier that tore through a Saint Petersburg supermarket and wounded 14 people.
"Investigators will be petitioning the court for his arrest", she said adding the suspect was questioned at the Investigative Committee.
Russian officials described the bomb as a home-made device packed with lethal components that produced a blast equivalent to 200g (7oz) of TNT.
Putin's 2015 decision to intervene in Syria militarily on the side of President Bashar al-Assad has made Russian Federation a priority target for IS.
Saint Petersburg, Russia's former Imperial capital, will host World Cup matches next year.
"What would have happened if those hundreds, thousands. had come back to us, trained, armed and well-prepared?" he said.
The bombing follows April's suicide attack in the St Petersburg metro which killed 15 people. Russian authorities founded the bomber as a 22-year old Kyrgyz-born Russian nationalized.
Earlier this month, Putin declared victory in Syria and ordered a partial withdrawal of Russian troops from the country.
Mr Putin thanked President Trump for help from the Central Intelligence Agency in identifying the suspects.