Turkey's deputy prime minister has offered a partial apology for the vicious police crackdown on protesters in Istanbul, in an apparent attempt to cool tensions after nine days of anti-government rallies across Turkey.

Bülent Arinç, who is standing in for Turkey's absent prime minister, Recep Tayyip Erdogan, said the violence meted out last week to peaceful protesters was "wrong and unjust". He also offered to meet leaders of the original movement, which began in an effort to save an Istanbul park from redevelopment.

But it was unclear if Arinç's conciliatory remarks had the blessing of Erdogan, who has previously dismissed the protesters as "looters" and fringe extremists. Erdogan is on a visit to Morocco. His abrasive response has infuriated secular middle-class Turks, who have taken to the streets to oppose him in unprecedented numbers, with protests spreading rapidly across the country.

For the first time, the protesters also offered to abandon their occupation of Gezi park and the nearby Taksim Square in Istanbul, the focal point of a broad-based anti-Erdogan movement. They issued a list of demands. These included the prompt release of hundreds of people arrested in the turmoil of the past week, an end to park development and the resignation of officials who abused their positions by giving orders that resulted in injuries.

On Tuesday, thousands more demonstrators packed into the square, gathering under the trees and around a statue of Turkey's secular founder, Mustafa Kemal Atatürk, now decorated with banners. The authorities had vacated the area, leaving barricades and piles of rubble in place.

"We are sending Erdogan a message. The message is: 'You are not a king in this country. We are the kings here'," said Murat Özerden, an Istanbul businessman.

There were some signs that the violence of the past five days, driven by over-the-top policing, could be abating.

Istanbul's police chief said his forces would only use teargas as a last resort. Beskitas football supporters, who have figured in previous clashes near the prime minister's office, added that they would march peacefully to the square.

The protesters are aggrieved by what they perceive as Erdogan's authoritarian tendencies and his attempts to impose a more Islamic lifestyle on all citizens. He has recently passed a law to restrict alcohol consumption. Others are upset by his pro-rebel foreign policy towards Syria, and his warm relations with the US, Turkey's strategic ally.

There is much at stake in the standoff, which represents the biggest challenge to Erdogan in a decade. "Whether this drama ends with a compromise or further escalation will likely define the next decade of Turkish politics, which faces a cycle of municipal, presidential and parliamentary elections over the next two years," the International Crisis Group said in an analysis.

One prominent critic said Erdogan was personally to blame for the unrest. Selahattin Demirtas, a member of the pro-Kurdish Peace and Democracy party (BDP), said: "The reason for these protests are not foreign or domestic forces, but the result of only trying to satisfy one half of the country and ignoring the other half."

He added: "The person who lit the spark that set the whole country aflame was the prime minister."

The main public-sector union federation, KESK, which represents 240,000 members, began a two-day strike on Tuesday in support of the protesters, while a second group, the Turkish Revolutionary Workers' Union Confederation, said its members would also stage a walkout on Wednesday.

Speaking on Tuesday, Arinç conceded that the original police decision to storm a camp of eco-activists on Friday was a mistake. "I apologise to those citizens," he said. He said Turkey's government was sensitive to the demands of the country's secular urban classes, most of whom had not voted for Erdogan's Islamist-rooted Justice and Development party (AKP). "I would like to express this in all sincerity: everyone's lifestyle is important to us and we are sensitive to them," he declared.

Arinç spoke after a meeting with President Abdullah Gül. In contrast to Erdogan, Gül has sought to mediate with the protesters, and has skilfully praised them for expressing their democratic rights. Since the crisis began he has emerged as a leading moderate, and could face Erdogan next year in a presidential election.

There have been several deaths at the protests, including that of a 22-year-old man shot on Monday in the city of Antakya. Prosecutors later said the man had died from a blow to the head. The Foreign Office on Tuesdayurged British nationals to avoid demonstrations in Turkish cities, and warned that "further violent protests remain possible".

A human rights group, Turkish Human Rights Association, has said some 1,000 protesters have been subjected to "ill-treatment and torture". The UN human rights office in Geneva has expressed concern about the excessive use of force by police and called on Turkey to respect the right to peaceful protest and to promptly investigate abuses and bring perpetrators to justice. It also called on protesters to remain peaceful.

The Turkish Human Rights Association said some 3,300 people nationwide were detained during four days of protests, although most have since been released. At least 1,300 people were injured, the group said, although it said accurate figures were difficult to come by.