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Russian President Vladimir Putin said the US Congress had no right to approve the use of force against Syria without a decision from the UN Security Council, and that doing so would be an "act of aggression".
President Obama said he believes Congress will approve military action against Syria.
During a one-day visit to Sweden, he said: "I think America also recognises that if the international community fails to maintain certain norms, standards, laws governing how countries interact and how people are treated, that over time this world becomes less safe."
President Obama said the US wanted to "join with the international community in an effective response" that deters the use of chemical weapons in the future.
He said: "I respect the UN process. Obviously the UN investigation team has done heroic work under very difficult circumstances but we believe very strongly, with high confidence, that in fact chemical weapons were used and that Mr Assad was the source.
"We want to join with the international community in an effective response that deters such use in the future."
President Obama said he discussed the "appalling violence being inflicted on the Syrian people by the Assad regime including the horrific chemical weapons attacks" with the Swedish Prime Minister during a one-day visit to the Scandinavian country.
He said: "I discussed our assessment which clearly implicates the Syrian Government in this outrage.
"The Prime Minister and I are in agreement that in the face of such barbarism the international community cannot be silent and that failing to respond to this attack would only increase the risk of more attacks and the possibility that other countries would use these weapons as well."
Former US Secretary of State Henry Kissinger said it would be a "catastrophe" if Congress did not back military action and "undermine the American position in the world" after Mr Obama made the use of chemical weapons a "red line" issue.
He told BBC Radio 4's Today programme action should be more than a "shot across the bows" but not go as far as intervening to influence the result of the civil war.
The chairman of the Senate Foreign Relations Committee has said that a new draft resolution ensures that any military action in Syria would be "narrow and focused".
Democratic Senator Robert Menendez, who drafted the resolution with the committee's top Republican, said in a statement:
A revised draft resolution setting the parameters of any intervention in Syria has been agreed by the US Senate Foreign Relations Committee, but is still subject to votes.
The document is due to be voted on by the committee on Wednesday and, if approved, will be sent to the full Senate for a vote after members return on 9 September.
A new US draft resolution authorising military force in Syria puts a 60-day limit on any intervention, with the possibility of extending this once by 30 days, the Associated Press reports.
It also expressly bars the use of US ground forces for "combat operations".
US President Barack Obama will hold bilateral meetings with Chinese premier Xi Jinping and French President Francois Hollande on the sidelines of the forthcoming G20 meeting, a White House official has told Reuters.
There are no plans for a formal bilateral meeting between Obama and Russian President Vladimir Putin, the official said, noting the two presidents may speak "on the margins" of meetings held during the summit.
Latest ITV News reports
Obama made a personal appeal to the international community to unite in military action against 'barbarism' in Syria.
President Obama has received the support of prominent Republicans as he tries to gain backing for military action in Syria.