Corpses of activists were seen strewn across the ground after the blasts, with the banners they had been holding lying next to them.
At least 30 people were killed and 126 wounded, the interior ministry said in a statement giving the first official toll.
"We curse and condemn this atrocious attack taking aim at our democracy and our country's peace," the statement said.
A Turkish government official said that the authorities "suspect that there is a terrorist connection," without giving further details.
There were scenes of chaos after the blast, as ambulances searched for the wounded and police cordoned off the area.
"We heard one huge blast and then one smaller explosion and then there was a a great movement and panic. Then we saw corpses around the station," said Ahmet Onen, eyewitness.
"A demonstration that was to promote peace has turned into a massacre, I don't understand this," he said, in floods of tears.
Turkish police fired in the air to disperse demonstrators angered by the deaths of their fellow activists from the scene, eyewitnesses said.
Initial reports spoke of a single explosion but Turkish media said later there had been two separate blasts in short sequence.
The authorities were exploring the possibility that the blasts could have been caused by a suicide bomber, the official Anatolia news agency said. /End/