"We all need to be mature in order for the protests... which have reached a worrisome level, to calm down," Gul said in a statement released by his office, calling on the police to "act in proportion".
Turkey's government appeared to be trying to placate demonstrators on the second day of anti-government demonstrations, even as police let off more tear gas and pressurized water against protesters in the capital, Ankara.
The protests grew out of anger at heavy-handed police tactics to break up a peaceful sit-in by people trying to protect a park in Istanbul's main Taksim square on Friday.
Bulent Arinc, the deputy prime minister, said the government was wrong to break up the peaceful protest with tear gas and said he welcomed a court's decision that suspended the uprooting of the park.
"It would have been more helpful to try and persuade people who said they didn't want a shopping mall instead of spraying them with tear gas," Arinc told reporters.
The park demonstration turned into a wider protest against Prime Minister Recep Tayyip Erdogan, who is seen as becoming increasingly authoritarian, and spread to other Turkish cities despite the court decision to temporarily halt the demolition of the park.
A human rights group said hundreds of people were injured in scuffles with police that lasted through the night.