US Secretary of State Hillary Clinton has warned that sharp divisions remain with Moscow over Syria as she wrapped up an Asia tour in which she also made little headway with China on easing tensions in the South China Sea.

Mrs Clinton said she had made the case for increasing pressure on Syrian President Bashar al Assad in talks with Russian President Vladimir Putin and Foreign Minister Sergei Lavrov, but was pessimistic about the chances of closing the gap before the UN General Assembly this month.

"If we can make progress in New York in the run-up to the UN General Assembly, we can certainly try," Mrs Clinton told reporters in Vladivostok, where she attended a Pacific Rim summit hosted by Mr Putin.

"But we have to be realistic. We haven't seen eye-to-eye on Syria. That may continue. If it does continue then we will work with like-minded states to support the Syrian opposition to hasten the day when Assad falls."

On her 11-day Asia trip, Mrs Clinton sought to push for more forceful international steps on Syria, greater unity over Iran's nuclear programme and a multilateral mechanism for China to deal with maritime territorial disputes with its south-east Asian neighbours.

But the Chinese and Russians restated their opposition to what they see as US meddling. "Our US partners prefer measures like threats, increased pressure and new sanctions against both Syria and Iran. We do not agree with this in principle," Russia's Lavrov said after talks with Mrs Clinton.

Mr Putin said that although his talks with Mrs Clinton had been had been constructive and useful, they had yielded no agreements.

Mrs Clinton said she would continue to work with Mr Lavrov to see if the UN Security Council could formally endorse an agreement brokered by former UN Syria envoy Kofi Annan that envisages a transitional governing authority for Syria.

But she added that such a step would only be effective if it carried specific penalties if Mr Assad fails to comply, something Russia has repeatedly resisted.

"There's no point passing a resolution with no teeth because Assad will ignore it and keep attacking his own people," Mrs Clinton said.

When the agreement Russia wants the Security Council to endorse was reached in late June, it left open the question of what part Mr Assad might play in a Syrian political process. Russia says his exit must not be a precondition forced from outside.