The military said the first bomber ran into the market, attracting people towards him by claiming he was feeling unwell.
Yesterday's attack was the bloodiest incident in Baghdad since January 2018, when a suicide bomber - also in Tayaran Square - killed more than 30 people.
Thursday's twin attack was not immediately claimed but suicide bombings have been used by ultra-conservative militant groups, most recently the Islamic State (IS) organisation.
Thursday's twin suicide bombings marked the first in three years to target Baghdad's bustling commercial district.
The health ministry said those who lost their lives had died on the scene of the attack, and that most of the wounded had been treated and released from hospital.More news: Donald Trump's Facebook ban could be lifted by Oversight Board
After years of deadly sectarian violence, suicide bombings have become relatively rare in the capital.
An Interior Ministry spokesman said the death toll had risen to at least 28, and that number was expected to rise as some wounded were in critical condition.
Militias have routinely targeted the American presence with rocket and mortar attacks, especially the US Embassy in the heavily fortified Green Zone. The pace of the attacks has decreased since an informal truce was declared by Iran-backed armed groups in October.
Elections in Iraq are typically preceded by escalating violence, including bombings and assassinations.
The 2018 attack took place just months before parliamentary elections and Iraq is planning another general election later this year.
The IS seized a third of Iraq in 2014 and was dangerously close to the capital, but a ferocious three-year fight by Iraqi troops pushed them back.More news: Can COVID-19 vaccines be mixed and matched?
The hardline Sunni Muslim group captured vast areas of Iraq and imposed its own rule before being defeated in 2017 by Iraqi forces backed with US air power.
Thursday's attack shattered a sense of relative security in the capital, raising questions over the Iraqi security forces' preparedness in the face of a militant threat diminished but by no means erased.
Prime Minister Mustafa al-Kadhimi had announced in July that early polls would be held to meet the demands of anti-government protesters.
The United States, which provides the bulk of the force, has 2,500 troops left in Iraq - down from 5,200 a year ago.
Demonstrators took to the streets in the tens of thousands past year to demand political change, and an end to rampant corruption and poor services.
But authorities are in talks to reschedule them for October in order to give electoral authorities more time to register voters and new parties. The Central Bank of Iraq devalued Iraq's dinar by almost 20% llast year to meet spending obligations.More news: United Kingdom records its deadliest day of the coronavirus pandemic