TV footage showed scenes of panic and people lying on the ground covered in blood, amid protest banners.
The twin blasts took place near Ankara’s central train station as people gathered for a march organized by leftist groups.
The attack is the deadliest of its kind in modern Turkish history.
PM Ahmet Davutoglu has announced three days of national mourning, and said there was evidence that two suicide bombers had carried out the attacks.
President Recep Tayyip Erdogan said the attack, which comes weeks before an election, was an act of terrorism and was “loathsome”.
The rally was demanding an end to the violence between the Kurdish separatist PKK militants and the Turkish government, and had been due to start at 12:00 local time.
The pro-Kurdish HDP party was among those attending, and it said in a statement that it believes its members were the main target of the bombings.
The leader of the HDP has blamed the state for the attack, which he called “a huge massacre”, and cancelled all election rallies.
The party has previously blamed the government for colluding in attacks on Kurdish activists, which the government denies.
The two explosions happened shortly after 10:00 local time as crowds gathered ahead of the rally. Amateur video footage showed a group of young people holding hands and singing, before the first blast.
Meanwhile, the PKK called on its fighters to halt its guerrilla activities in Turkey unless attacked first. A statement from an umbrella group that includes the PKK said its forces would “make no attempts to hinder or harm the exercise of a fair and equal election”.
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