Speaking at the scene of the bombings, Salman said the death toll had risen to 28 from 23 initially reported, with 73 more people wounded.
Police sources said Iraqi security forces had been deployed and key roads blocked to prevent possible further attacks.
Suicide bombings were once common in Baghdad but have been rare in the Iraqi capital since Islamic State was driven out. The last deadly suicide blast in the city, also at Tayaran Square, killed at least 27 people in January 2018.
Reuters cameramen saw pools of blood at the scene shortly after the blast.
“The attacker was standing in the middle of a crowd and pretended to be sick, and then blew himself up and tore people to pieces,” said a street vendor who had been standing nearby.
A video taken from a rooftop and circulated on social media purported to show the second blast scattering people gathered in the area. Images shared online showed several people apparently dead or wounded.
Reuters could not independently verify those images.
Militants from Islamic State remain in Iraq, waging an insurgency against Iraqi forces and attacking local officials in northern areas. Government and military officials do not now consider the group able to take over significant territory but say it will continue to wage attacks that threaten Iraq’s stability and security.
Iraqi forces continue to fight remaining Islamic State militants and are working to secure the border with Syria across which the group has often moved personnel.