Democratic presidential candidate Hillary Clinton called for a sharp increase in the number of Syrian refugees the U.S. accepts, up to 65,000 from the current level of between 5,000 and 10,000.

The former secretary of state’s appeal to raise the cap on Syrian refugees came as Secretary of State John Kerry announced in Berlin that the U.S. will increase the number of refugees it accepts to 100,000 in fiscal year 2017, up from 70,000 a year currently.

“I...