Recep Tayyip Erdogan said he would not yield to “wild extremists” and urged an end to the protests.
Clashes over Taksim Gezi Park in Istanbul began on Friday and continued there and in the capital, Ankara, on Saturday.
Correspondents say the local issue has spiraled into more widespread anger over perceived “Islamisation”.
Recep Tayyip Erdogan has been in power since 2002 and some in Turkey have complained that his government is becoming increasingly authoritarian.
His ruling AK Party has its roots in political Islam, but he says he is committed to Turkey’s state secularism.
Last week, Turkey’s parliament approved legislation restricting the sale and consumption of alcoholic drinks between 22:00 and 06:00.
In a defiant speech to the exporters’ union, Recep Tayyip Erdogan insisted that the park project would go ahead.
“We will rebuild the [Ottoman era military] barracks [at the site],” he said, without referring to the shopping mall that protesters fear will be located there.
Opponents say Gezi Park in Taksim Square is one of the few green areas left in central Istanbul.
Recep Tayyip Erdogan vowed order would be restored “to ensure the safety of people and their property”.
He said: “Police were there [Taksim Square] yesterday; they’ll be on duty today and also tomorrow because Taksim Square cannot be an area where extremists are running wild.”
Recep Tayyip Erdogan accused protesters of using the issue as an excuse to create tension and called on them to end their action immediately to avoid “further damage to visitors, pedestrians and shopkeepers”.
He said of the protests: “All attempts apart from the ballot box are not democratic”, adding that he could summon a million pro-government protesters if he wanted to.”
However, the prime minister did admit that the police response may have been “excessive” and that “necessary instructions” had been given to the minister of the interior and the governor of Istanbul.
The protest began on Friday as a sit-in over the redevelopment plans but escalated after police used tear gas. A dozen people were admitted to hospital and more than 60 people detained.
On Saturday, hundreds of demonstrators marched over the bridge connecting the Asian and European shores of Istanbul to try to reach the main square.
Police fired tear gas to try to disperse them and some protesters threw rocks.
Police also fired water cannon and tear gas in Taksim Square as demonstrators chanted “unite against fascism” and “government resign”.
Clashes were also reported in the Besiktas district.
One Istanbul resident, who gave her name as Lily, revealed that police had dropped tear-gas canisters from helicopters overnight.
“About half past one the entire city started to reverberate. People were banging on pots, pans, blowing whistles,” she said.
One woman protesting in Istanbul told Agence France-Presse: “They want to turn this country into an Islamist state, they want to impose their vision all the while pretending to respect democracy.”
In Ankara on Saturday, hundreds of demonstrators gathered at a park, many drinking alcohol in protest at the new restrictions.
Some chanting anti-government slogans tried to march on parliament but were dispersed by police.
Many postings on Twitter have complained angrily about the lack of media coverage of the protests within Turkey.
The US has expressed concern over Turkey’s handling of the protests and Amnesty International condemned the police’s tactics.
In his speech, Recep Tayyip Erdogan criticized the “preaching” of foreign governments, saying they “should first look at their own countries”.
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