Brief scuffles broke out between the crowd and the police after some mourners tried to lay carnations at the site of the bombings.
The pro-Kurdish HDP party, which organised Saturday’s rally, said 128 people were killed in the attacks.
Protesters have blamed the government for security failures around the rally.
The government has rejected suggestions that it was to blame for the bombing.
Prime Minister Ahmet Davutoglu said there was evidence that two suicide bombers had carried out the attack.
Turkey declared three days of mourning after Saturday’s attack, the deadliest ever in Turkey.
The attack, at a peace rally, left 245 people injured, with 48 of them in a serious condition.
TV footage showed scenes of panic and people lying on the ground covered in blood, amid protest banners.
People are now concerned about the escalation of violence and about maintaining security ahead of a re-run of June’s inconclusive parliamentary elections due to be held in three weeks’ time, our correspondent says.
The blasts took place near the city’s central train station as people gathered for a march organised by leftist groups demanding an end to the violence between the Kurdish separatist PKK militants and the Turkish government.
The two explosions happened shortly after 10:00 as crowds gathered ahead of the rally. Amateur video footage showed a group of young people holding hands and singing, as the first blast hits.
No group has said it carried out the attack, but Mr Davutoglu suggested that Kurdish rebels or the Islamic State (IS) group were to blame.
Terrorism experts have said the attack is similar to one that was carried out in Suruc in southern Turkey by IS in July in which 30 people died, our correspondent says.
However, the leader of the HDP party, whose members were among those attending the rally, has blamed the state and cancelled all election rallies.
An HDP rally in the city of Diyarbakir was bombed in June, ahead of general elections in which the party entered parliament for the first time.
The party has previously blamed the government for colluding in attacks on Kurdish activists, which the government denies.
Cemalettin Hasimi, director of press and information at the prime minister’s office, told the BBC that such allegations were “a disgrace, unacceptable”.
A ceasefire between the PKK and Turkey’s government broke down after the attack in Suruc, with the PKK accusing the security forces of collaborating with IS.
This led to an increase in attacks from both sides over the summer.
On Saturday, the PKK declared a unilateral ceasefire, calling on its fighters to halt its guerrilla activities in Turkey except in cases of self-defence.
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”.
But on Sunday, the Turkish military said it had carried out air strikes against the PKK group, attacking targets in south-eastern Turkey as well as PKK positions in northern Iraq and killing 49 people.