Police said they had arrested one man after the attack, which killed four people and injured 15, while Swedish Prime Minister Stefan Lofven yesterday said "everything pointed" to it being a terror attack.
US State Department acting spokesman Mark Toner condemned "this brutal and senseless attack" and said the United States was ready to provide any assistance it could to investigate it.
"Attacks like this are intended to sow the seeds of fear, but in fact they only strengthen our shared resolve to combat terrorism around the world," Toner said in a statement.
"We hope that those responsible for the attack will be swiftly brought to justice," he said.
European Commission President Jean-Claude Juncker said the attack was a blow struck against all EU countries.
"An attack on any of our member states is an attack on us all," Juncker said in a message of condolences to the victims, adding the aim appeared to strike at "our very way of life."
Antonio Tajani, the head of the European Parliament, said on Twitter that he was "shocked by the terrible news from Stockholm."
"Britain's thoughts are with the victims, their families and the whole of Sweden," he said.
President Francois Hollande expressed his "horror and indignation" at the attack.
"France expresses its sympathy and solidarity with the families of the victims and all Swedes," he said.
Paris Mayor Anne Hidalgo announced on Twitter that the Eiffel Tower, which is normally illuminated, would go dark for a minute at midnight in honour of the victims of the attack.
Chancellor Angela Merkel's spokesman said Germany stood "together against terror" with Sweden, and offered sympathy for those involved in the attack.
"Our thoughts are with the families of the victims and the people of Sweden."
Dutch Prime Minister Mark Rutte called the attack "terrible news" and said he had conveyed his country's condolences to his Swedish counterpart.
"Our thoughts go out to the victims and survivors," he said in a message on his Twitter account. "NL stands ready to help where needed."
"In our country, we are well familiar with the crimes of international terrorism. At this difficult time, Russians weep with the Swedish people," President Vladimir Putin said in a statement.
"Condolences to the victims and best wishes for recovery to the wounded. We stand by your side Sweden," he said in a Twitter message.
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