As protesters meet with a top leader, others are arrested because of their social media activity. (Burhan Ozbilici/AP)

Organizers of the protests that have gripped Turkey since last week presented demands Wednesday to the deputy prime minister, as police detained more than two dozen people accused of provoking violence on social media.

With Prime Minister Recep Tayyip Erdogan out of the country until Thursday, the meeting with his deputy, Bulent Arinc, was a small concession to the tens of thousands of protesters who have posed the largest challenge to Erdogan’s power in his 10 years in office.

But there was no immediate response to the demands, and protesters dug in awaiting Erdogan’s return. Although the demonstrations in Istanbul remained largely peaceful Wednesday, there were reports of clashes with police in Ankara and continued protests in other cities.

Police also arrested 25 people in the coastal city of Izmir late Tuesday, accusing them of inciting illegal actions by calling for protests on social media, the state-run ­Anadolu news agency reported. The arrests sparked furious reactions on Twitter, which many protesters are using to spread information and news after Turkish media sympathetic to Erdogan’s Justice and Development Party were slow to report on the unrest.

Protest organizers said in a televised statement after meeting with Arinc that they wanted an end to police violence, immediate freedom for the thousands detained since demonstrations began Friday and a repudiation of plans to raze the last park in the center of Istanbul to make way for commercial development.

The threat to Gezi Park was the spark for the turmoil that has spread across Turkey in recent days. Police initially cracked down hard on the protesters, using tear gas and batons to dispel them. But that only inflamed the situation, bringing more people to the streets. Before Erdogan left for a goodwill trip to Africa on Monday, he dismissed the protests, saying they were led by “extremists,” and announced that he wanted to erect a mosque in the surrounding Taksim Square.

Another Erdogan deputy said Wednesday that the government was trying to soften its response to the protests, which have left two people dead and more than 2,000 injured.

“We are working towards reading protesters’ messages in a better way,” Deputy Prime Minister Besir Atalay said in remarks carried by Anadolu.

In a Wednesday phone call, Foreign Minister Ahmet Davutoglu told Secretary of State John F. Kerry that Turkey was not a ­“second-rate democracy,” the news agency said, pushing back against U.S. criticism of the crackdown on protesters.

It remained far from clear whether the protests could disrupt Erdogan in a deeper way. Many of the middle-class demonstrators who crowded Taksim Square on Wednesday evening said they did not want his ouster. And with several fiery speeches being delivered all at once by speakers in different corners of the square, protesters remained divided among themselves: political parties vs. those who abhor politics; Kurds vs. Turks; anarchists vs. those who like to sip espressos in Istanbul’s upscale cafes.

“It is kind of a Woodstock. It is not Tahrir,” said Betul Tanbay, a math professor, referring to Cairo’s central square, the nucleus of protests that brought down Egypt’s authoritarian ruler two years ago. Tanbay is one of the founders of the Taksim Solidarity Platform, the group that met with Arinc in Ankara on Wednesday.

Relatively few protesters are seeking a revolution to overthrow Erdogan. Nor does the movement have the backing of religious conservatives, a powerful constituency in Egypt and Turkey that was crucial to the downfall of Egyptian President Hosni Mubarak.

Instead, Tanbay said, the protest in Istanbul is festive. “It is a big youth movement now,” she said.

In Taksim Square, the only fumes in the air Wednesday came from vendors grilling kofte meatballs, a sharp change from earlier this week, when police repeatedly used tear gas against protesters. Some men sold neon swim goggles just in case the tear gas returned. Another man performed a Sufi dervish dance wearing a gas mask.

Trade unionists marched with banners calling for Erdogan to resign; others relaxed and listened to songs that poked fun at the prime minister’s characterization of protesters as “losers.”

“Our lifestyle is in danger,” said Yeniz Karaca, 30, who was strolling through Gezi Park on Wednesday evening, ticking off a list of the changes in recent years. First, more women started wearing head scarves, long a taboo in secular Istanbul. More recently, Erdogan instituted restrictions on drinking alcohol in public. “He is taking us back to the Ottoman Empire. Little by little, everything is forbidden,” she said.

“We go to work. After work, we come here,” Karaca said, asking that details about her white-collar profession not be published because she feared losing her job. “If we were free, we would not be afraid,” she said.

Across Istanbul, in a middle-class section of Kadikoy, the Asian side of the city, many were sympathetic to the protesters’ goals.

“I have never seen violence like this on civilians,” said Ozgur Alacan, 34, an architect who has been banging on a pot at her window every evening, along with many others, to show solidarity with the protesters. The demonstrations, she said, will last “until the people who are doing this realize their mistake.”