The Syrian Democratic Forces, a Kurdish-Syrian Arab alliance fighting the Islamic State group, "have made the decision to ask the civilians to depart, as opposed to staying in Raqqa," Dillon said.
The SDF is closing in on Raqqa from the north, west and east, but has not yet battled its way to areas south of the city.
Meanwhile, Russian aircraft have carried out a series of strikes against IS convoys fleeing the city, Moscow said on Thursday.
The first airstrike targeted IS convoys leaving their de-facto capital as they headed south to Palmyra on 25 May and overnight from 29 to 30 May.
The second destroyed dozens of cars and pickup trucks and killed scores of IS fighters.
The news comes after Russia fired four cruise missiles from a submarine and warship in the Mediterranean Sea at IS fighters who had moved close to Palmyra from Raqqa.
Russia has been flying a bombing campaign in Syria since 2015 in support of President Bashar al-Assad, while the US has been leading a coalition mainly targeting IS.
More than 320,000 people have been killed and millions displaced by Syria's conflict, which erupted in March 2011 with protests against Assad.
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