Turkish Prime Minister Recep Tayyip Erdogan said Friday his Islamic-rooted government was open to "democratic demands" as he hit back at EU criticism of his handling of a week of deadly unrest.

Erdogan accused international allies of double standards after European Union Enlargement Commissioner Stefan Fule called for a "swift and transparent" probe into police abuses against anti-government protesters in Turkey, a longtime EU hopeful.

"Peaceful demonstrations constitute a legitimate way for these groups to express their views," Fule said at an Istanbul conference attended by Erdogan. "Excessive use of force by police against these demonstrations has no place in such a democracy."

In a sharp retort, the combative premier said: "In any European country, whenever there is a violent protest against a demolition project like this, believe me, those involved face a harsher response."

Turkey's trouble began when police cracked down heavily on a small campaign to save Istanbul's Gezi Park, spiralling into nationwide demos against Erdogan and his Justice and Development Party (AKP), seen as increasingly authoritarian.

Police used tear gas and water cannon to disperse demonstrators, injuring thousands and leaving three dead in mass unrest that has thrown up the biggest challenge to Erdogan's decade in power.

Erdogan, who has dismissed the demonstrators as vandals and extremists, on Friday said that he was "against violence", adding in a more conciliatory tone: "I'm open-hearted to anyone with democratic demands."

Defying Erdogan's latest call to end the protests, thousands massed peacefully on Istanbul's Taksim Square for an eighth night, gathering in a festive atmosphere to a soundtrack of drums and pipe music. Large crowds also took to the streets of the capital Ankara, with no reports of confrontation.

"We need democracy in Turkey, that's why we come to Taksim Square," Burhan Ozdemirci, 30, told AFP as he sipped a beer on the square, the epicentre of the protests.

Bracing for Erdogan's reaction to their continued demonstrations, many said they felt safe in Taksim, which has seen no police presence since police pulled out of the site last Saturday.

"Taksim is our palace," said 21-year-old student Eray Dilek, adding that he was more nervous for protesters gathering in other cities.

In a bid to boost their profile, supporters of the protest movement raised more than $100,000 in an online fundraising drive to run a full-page ad in the New York Times Friday to explain why the demonstrators are so furious.

"People of Turkey have spoken: we will not be oppressed," read the ad, saying that during Erdogan's 10 years in power Turks have seen their civil rights and freedoms erode, with many journalists, artists and elected officials arrested.

Erdogan has likened the trouble in Turkey to the Occupy Wall Street movement that sprang up in the United States in 2011 and inspired copycat protests in European cities.

But the US embassy in Ankara wrote on its Twitter feed on Friday: "No US deaths resulted from police actions in #OWS."

Erdogan's slightly softer stance appeared to calm investors on Friday. The Istanbul stock exchange's main index partially recovered heavy falls earlier in the week to close 3.21 percent higher.

Analysts warn that the unrest risks scaring off the foreign financing on which Turkey's recent economic development has largely relied.

-- 'We will die for you, Erdogan' --

The national doctors' union says 4,785 people have been injured in the countrywide protests, 48 of them severely.

The unrest has left three people dead -- two young protesters and a policeman, according to officials and doctors.

Critics accuse Erdogan of forcing conservative Islamic values on Turkey, a mainly Muslim but staunchly secular nation.

Jailed Kurdish rebel chief Abdullah Ocalan on Friday voiced his support for the anti-government protests, despite his involvement in peace talks with the Turkish authorities.

NATO member Turkey has long sought to join the 27-member EU block but efforts have stalled in recent years, with reticence over the country's human rights record a key stumbling block.

But in a reassuring move, Fule, the EU's top official on the issue, said the bloc was sticking by the country's membership bid.

While opposition to the premier is intense, the 59-year-old Erdogan has won three elections in a row and gained almost 50 percent of votes in 2011, having presided over strong economic growth.

Supporters of Erdogan and his AKP party have stayed mainly silent as the protests raged, but they cut loose early on Friday when they flocked to Istanbul's main airport to welcome the premier home from an overseas trip.

"We will die for you, Erdogan," they chanted, waving red and white Turkish flags and threatening the liberal demonstrators with the refrain: "Let us go and crush them all."

After praising loyalists for their restraint so far, Erdogan encouraged them to "go home".