"I pressed that we must see the last removal of the 8 percent remaining at a site near Damascus," Kerry told reporters, saying the telephone conversation took place during his flight to Democratic Republic of Congo on Saturday.
"We agreed that we would work on certain things to try to see if it is possible to accelerate that process with an understanding that the government of Syria cannot delay," he said, without elaborating.
Syria has been removing 1,300 tons of chemical weapons under a deal reached last year which averted Western military strikes, after a sarin gas attack on suburbs around the Syrian capital in August.
Syria's Western foes accuse the government of deliberately dragging out the process, but a militant advance east of Damascus shows there are genuine obstacles to getting the chemicals out.
Still, Kerry put the onus on the Syrian government to prepare the weapons for removal.
"They must move immediately to prepare those remaining chemical weapons for removal and we need to meet that removal as fast as possible," he said.
Syria has been gripped by deadly unrest since 2011. According to reports, Western powers and their regional allies - especially Qatar, Saudi Arabia, and Turkey - are supporting the militants operating inside the country.
NTJ/HH