Barack Obama also said that the international community "cannot be silent" following Syria's alleged use of chemical weapons against its own people.
"I discussed our assessment and (Swedish Prime Minister Fredrik Reinfeldt) and I are in an agreement that in the face of such barbarism the international community cannot be silent," he said.
He also stated that he was not the one to set a Red Line, but the world itself set a Red Line against the use of chemical weapons.
"Credibility of the US, Congress, and International Community is on the line - not mine - in need to uphold chemical weapons ban and respond to Syrian attack," Obama said. "We must send a real strong message to Assad and to degrade his ability to use chemical weapons again with action limited in time and scope".
The US president said that the country won't repeat mistakes of Iraqi war and that evidence was clear that Syrian government used chemical weapons.
US President Barack Obama arrived in Sweden on Wednesday en route to an economic summit in Russia where the Syrian civil war is expected to dominate the discussions.
Obama is the first incumbent US president to make a bilateral visit to Sweden. The trip was announced in August, shortly after he cancelled a meeting with his Russian counterpart following Moscow's asylum offer to fugitive US whistleblower Edward Snowden.
A massive security detail was in place in the Swedish capital, Stockholm, for the roughly 24-hour visit. An estimated 2,000 police officers, some called in from other parts of the country, were part of the detail with US security agents.
"No to Big Brother Obama" was the overarching theme of a protest organized by the September 4 Network critical of US surveillance operations disclosed by Snowden and others.
While Obama was en route to Stockholm, Russian President Vladimir Putin hinted for the first time that Moscow might back a UN resolution for military intervention in Syria.
That conflict was also likely to feature during Obama's meeting with Swedish Prime Minister Fredrik Reinfeldt, who has invited Nordic leaders to a working dinner.
Of the attending leaders from Denmark, Finland, Iceland and Norway, only Danish Prime Minister Helle Thorning-Schmidt has said her government could support possible military action against Syria even without UN Security Council approval.
Reinfeldt told Swedish television, shortly before Air Force One touched down at Arlanda Airport at about 08:00 GMT, that he planned to discuss free trade, citing Sweden's dependence on foreign trade and exports.
Sweden is a member of the European Union that recently opened talks on a free trade deal with the United States.
Obama will next travel to the Russian city of St Petersburg on Thursday for the Group of 20 (G20) summit hosted by Putin.