Turkey's prime minister has climbed on top of a bus to give a fiery speech to thousands of his supporters, challenging increasingly angry anti-government protesters to beat his party at the ballot box after they flooded the streets for a 10th day of demonstrations.

On Sunday Recep Tayyip Erdoğan visited two cities where unrest has occurred and again condemned his detractors as a handful of looters and vandals.

In the southern city of Adana, where pro- and anti-government protesters clashed on Saturday night, Erdoğan greeted supporters before lashing out at his opponents in the polarised country.

"We won't do what a handful of looters have done. They burn and destroy …They destroy the shops of civilians. They destroy the cars of civilians," Erdoğan told supporters who had greeted him at the local airport. "They are low enough to insult the prime minister of this country."

He urged his supporters to avoid violence and predicted that his Islamic-rooted party would defeat his opponents during local elections in March. "I want you to give them the first lesson through democratic means in the ballot box," he said.

The nationwide anti-government protests were sparked by outrage over police use of force against an environmental protest in Istanbul on 31 May, and have grown into a display of discontent toward Erdoğan's government.

Many accuse the prime minister of becoming increasingly authoritarian after 10 years in power and of trying to impose his conservative, religious mores in the country, which is governed by secular laws. Erdoğan has rejected the accusations, insisting he respects all lifestyles and is the servant of his people.

He has repeatedly branded the protests as illegal efforts to discredit his government before local elections next year. He frequently refers to the 50% majority he received in the 2011 elections to dismiss the protest as attempts by a minority group to dominate a majority of his supporters.

"As long as you walk with us, the Justice and Development party administration will stand strong," Erdoğan said. "As long as there is life in my body, your prime minister and your party chairman, God willing, will not be deterred by anything."

He then travelled to the city of Mersin, where anti-protests have been held, to make a similar speech and to open new sports facilities, where he defended his government's democratic credentials, and criticised protesters for not taking to the streets to defend the rights of female students who were barred from studying at Turkish universities because of bans enforced by previous governments on Islamic-style headscarves. "What did you do for the freedom of those who couldn't go to universities?" he said.

Erdoğan was also scheduled to travel to the capital, where thousands of supporters were preparing to greet him in a show of force. The prime minister's refusal to moderate his tone caused dismay in Ankara, where thousands of protesters again gathered in a central square close to government offices, a day after police used tear gas and water cannons to oust them from the area.

"As the prime minister continues (with) his harsh style, the resistance also continues and is getting bigger," said Çağdaş Ersoy a 23-year-old student who joined the protests in Kizilay square. "He is making the resistance bigger without realizing it."

Riot police spray water on protesters in Kizilay square. Photograph: Zuma /Rex

Another protester, Cihan Akburun, said: "Erdoğan should not provoke the people. We invite everyone to common sense."

Tens of thousands of demonstrators gathered in Taksim Square, Istanbul, where a violent police crackdown on a sit-in to prevent the demolition of its Gezi park triggered the unrest. The government has vowed to proceed with plans to redevelop Taksim, replacing the park with a replica Ottoman barracks. It has since reconsidered plans to build a shopping mall.

In Adana on Saturday night, a pro-government group hurled stones at marching anti-government demonstrators, the state-run Anadolu agency said. Police evacuated women and children, but the protesters continued to clash with stones and batons.

It was the second time in the past 10 days of protests that pro- and anti-government protesters had fought with one another. On Thursday, party supporters attacked about 30 protesters in the city of Rize, on the Black Sea coast.

Three people have been killed in the protests, including a police officer in Adana who fell into an underpass that was under construction while chasing demonstrators. Thousands have been injured.

Erdoğan said the demonstrators had martyred the police officer, and defended the law-enforcement officers, dismissing calls by some protesters that officers engaged in abuse be sacked. "We won't sacrifice our police to their wishes," he said. "We cannot leave the streets for anarchists and terrorists to roam." The government had previously apologised for the excessive force used to roust the environmental protesters.

Erdoğan blamed the protests on forces that were trying to prevent Turkey's rise. "There are those who cannot stomach Turkey becoming greater and stronger," Erdoğan said. "They don't want any investments in Turkey."