The terrorists have claimed responsibility for numerous attacks without providing evidence as they come under strain in the Middle East, where they have lost the majority of the territory they once controlled.
Firefighters and police officers work at the site of a blast in a supermarket in Saint Petersburg on December 27, 2017.
IS' Amaq news agency said the attack was carried out by an "Islamic State-linked group". "The suspect has been handed over to Russia's Investigative Committee for further investigative procedures", the FSB said in a statement. Investigators revealed that the device comprised 200 grams (7 ounces) of explosives and was equipped with shrapnel to create more destruction.
Russian president has called Wednesday's explosion in St. Petersburg a "terror attack", according to local media on Thursday.
In April, a suicide bombing in St Petersburg's subway left 16 people dead and wounded more than 50.
The optimistic New Year's greeting comes a day after Putin's spokesman said that Moscow views the continued strain on Russian-U.S. relations as a major disappointment of the year.
Russian authorities identified the bomber as a 22-year-old Kyrgyz-born Russian national.
In his annual New Year's letter to world leaders, Russian President Vladimir Putin has expressed his hopes for improved bilateral ties with Europe and the West in the coming year.
President Vladimir Putin had earlier described the blast at the Perekrestok branch as a terrorist act.
Earlier Putin announced that monthly payments for the birth of a first child would be introduced as additional support for Russian families.