The explosion was captured by airport security cameras.
Russian President Dmitry Medvedev also spoke out on the crash, saying government officials should be held accountable for lax security measures. The attack left 35 people dead and nearly 200 injured.
Medvedev also called for full security checks at all major transportation hubs.
Airport management objected, saying transport police were responsible for the inspection of people coming into the international arrivals area, where the bombing took place.
The finger-pointing could undermine confidence in Russia's security ahead of Medvedev's high-profile appearance this week trying to attract investors at the World Economic Forum in Davos, Switzerland. Monday's attack also called into question Russia's ability to safely host major international events like the 2014 Winter Olympics in Sochi and the 2018 World Cup.
British businessman Mark Green said he walked by just moments before the blast.
"It was pretty horrific, there was a lot of people running out of the terminal in the arrivals area, some of them were injured, some screaming and some in shock," he said.
No group has claimed responsibility for the explosion, but suspicion has fallen on Islamic militants from Russia's southern border. In recent years they've struck subways, commuter trains and passenger planes.
The Associated Press contributed to this story.