How these talks influence the debate, if at all, is itself in question.
When asked Thursday while walking alone to dinner if any progress had been made on Syria, U.S. President Barack Obama said, "No, we talked about the economy."
Fervent debate n U.S., around the world
A sweeping international consensus seems unlikely as long as Russia -- which will host Syrian Foreign Minister Walid Muallem in Moscow on Monday, according to Syria's official SANA news agency -- and the United States maintain their firm positions
Kerry said this week, in Washington, that "at least 10 countries have pledged to participate" in a military intervention that Obama and French President Francois Hollande have urged. Yet that figure could well change.
Britain, normally a dependable U.S. ally in military affairs, has voted against joining any military action. And officials in France -- where polls show one in three people favor strikes -- have said they will wait until the United States decides on a course of action.
That won't come until after Congress weighs in, likely next week, on a measure authorizing strikes focused on degrading Syria's ability to use chemical weapons. While congressional leaders have backed Obama's call for action, most legislators are officially undecided so much that what happens is still anyone's guess.
"It weighs on me," said Sen. Dianne Feinstein, D-California, who added "it is conclusive" chemical weapons were used. "... There is no question that what (public reaction) is coming in is overwhelmingly negative."
Yet the president -- arguing that the world cannot afford a country to use such weapons against its own people without responding -- hasn't promised he'll abide by the vote in Congress. And Pentagon spokesman George Little said the Syrian government "should not take solace from the deliberative process that we are undertaking right now."
"We have time to adjust, if necessary, given conditions on the ground, given what the Syrian regime may or may not do in terms of movements of equipment and so forth," Little told reporters Thursday.
Whatever the United States decides, some world leaders are stumping against military action.
In a letter Thursday to Putin in his role as host of the G20 summit, Pope Francis urged a "peaceful solution through dialogue" and called an armed intervention a "futile pursuit."
Speaking from St. Petersburg, European Council President Herman Van Rompuy said that while the international community "cannot remain idle" in the face of Syria's apparent chemical weapons use, "there is no military solution to the Syrian conflict."
"Only a political solution can end the terrible bloodshed, grave violations of human rights and the far-reaching destruction of Syria," he said. "Too many lives have already been lost and too many people have suffered for too long and lost too much."