Turkey's Deputy Prime Minister Bulent Arinc said in a television interview that the government could use the Turkish Armed Forces (TSK) if the police failed to halt the unrest.
"What is required of us is to stop if there is a protest against the law. Here is the police, if not enough gendarme, if not enough TSK. These authorities exist in the laws," Hurriyet Daily News quoted Arinc as telling broadcaster A Haber.
Arinc said that "nobody should complain about the police" reaction to the subsequent nationwide street actions.
Clashes continued Monday in several parts of Istanbul, with opposition activists saying police fired water cannon at a hospital near central Taksim Square where demonstrators had taken refuge.
The activists also said online that some of them had been attacked by government supporters.
Local media reported that a mob shouting pro-government slogans attacked an office of the opposition Republican People's Party in Istanbul.
Five Turkish unions were holding demonstrations on Monday to protest the police violence around Saturday's clearance of the park camp, Hurriyet reported.
There was an excessive use of rubber bullets, tear gas and stun grenades, the Taksim Solidarity activists' group said, noting that women, children and elderly people were present.
The Turkish bar association said police have detained 441 people in connection with the weekend clashes.
Protests against the park's redevelopment project began on May 28, sparking wider demonstrations against what activists call the increasingly authoritarian rule of Prime Minister Recep Tayyip Erdogan.