Some demonstrators chanted: "The killer state will be held to account!"
Prime Minister Ahmet Davutoglu, however, rejected accusations by opponents that the government was to blame for the nearly simultaneous attacks Saturday, calling them "dangerous" and "dastardly."
He also denied that they were a result of Turkey's involvement in war in Syria and that the government was dragging the country into the Middle Eastern quagmire.
"These attacks won't turn Turkey into a Syria," Davutoglu said.
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Government opponents have also accused President Recep Tayyip Erdogan of fomenting violence and ethnic tensions to gain votes for the ruling party in Turkey's November 1 election an accusation that the Turkish leader rejects.
In the last election in June, a Kurdish party gained support from voters, taking away the ruling party's majority in Parliament and Erdogan wants that majority back.
Turkish investigators were close to identifying one of the two suicide bombers, the prime minister said today, adding that the Islamic State group was the "No 1 priority" of its investigation.
Today, Yeni Safak, a newspaper close to the government, said authorities investigating the bombings were focusing on the Islamic State group, comparing DNA samples of the suspected bombers with those obtained from the families of some 20 extremists they suspect could have carried out the attacks.
No one has claimed responsibility, but the attack bears similarities to a suicide bombing in July that killed 33 Turkish and Kurdish peace activists near the southern town of Suruc, which borders Syria. The government blamed that attack on the Islamic State group.