Turkish soldiers near the border returned fire into Syria following the attacks, security sources said.
Residents gathered near the site where the rockets hit, some of them calling for the local governor to resign and others shouting slogans against the government. Riot police were present, but there were no clashes.
"I cannot sleep, my son wakes up with nightmares, he cannot sleep. We aren`t safe here. We are afraid to stay in our houses," Ayse, a 46-year-old woman, told Reuters.
On an official trip to the province of Gaziantep near the border on Saturday, Prime Minister Ahmet Davutoglu promised that all necessary measures would be taken to prevent rocket fire into Kilis.
Turkey is part of the U.S.-backed coalition fighting Islamic State militants in Syria.
Officials have said Turkey may call on the U.S.-led coalition to take stronger action in its fight against Islamic State along the border to prevent further attacks.
Kilis, which is housing an estimated 110,000 Syrian refugees, has been repeatedly hit by rocket fire in recent weeks. On Friday two people were killed in a similar attack.
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