Earlier Wednesday, Medvedev fired top airport security officials. He accused transport police of "taking an absolutely passive position. At best, they are examining migrants, to check their registration and display their authority," in comments carried on Russian state TV.
Among the people he dismissed was Andrei Alexeyev, the head of the Interior Ministry's transport administration for the Central Federal District, he announced in his televised remarks.
"If people don't understand how to work, we'll find other people," Medvedev said, according the RIA-Novosti news agency.
Moscow is observing a day of mourning for the victims Wednesday, with flags flying at half staff. The government asked television stations to cancel entertainment programs as a mark of respect, RIA-Novosti said.
"We have to do all we can to influence, if not the ideology, then at least the social and economic roots of terrorism -- poverty, unemployment, illiteracy, parentlessness," Medvedev said in Davos. "And we have to be sure that global development is stable, safe, and just and fair."
At the end of his speech, he announced that he was cutting short his previously planned stay in Davos to head back to Moscow.
The blast occurred around 4:30 p.m. Monday at the entrance of Domodedovo Airport's international arrivals section.
A day later, authorities were still trying to tally the exact number of people injured in the blast.
RIA-Novosti said as many as 180 were hurt. The Russian Ministry of Emergency Situations said there were 110 wounded people still in hospitals.
Medvedev blamed security violations. "What happened at Domodedovo shows the airport lacked security," he said Tuesday. "It's unbelievable that such a huge amount of explosives were brought into the terminal. Those officials responsible for security at Domodedovo must be punished for their decisions. This is a terror attack, a grief, a tragedy."
It is not yet clear what impact a recent decision to shake up the Russian Transport Police, which is charged with protecting train stations and airports, may have had on the security perimeter at the airport Monday.
In August, Medvedev fired at least 12 generals in the Transport Police branch of the Ministry of Interior, as part of a broader reform of the Russian security services.
Domodedovo is 22 kilometers (14 miles) southeast of Moscow and is the largest of Moscow's three airports, as well as the busiest in terms of passenger traffic.
It was still not immediately clear who was responsible for Monday's blast. Previous terror attacks in Russia have been blamed on militants from the North Caucasus region.
Over the past decade, bombers have hit trains and planes operating in and traveling out of Moscow at least four times, with a combined death toll of more than 100 victims.
In 2004, two planes blew up nearly simultaneously after taking off from Domodedovo airport. That attack was linked to Chechen suicide bombers.
An explosive device derailed an express train in November 2009, killing at least 26 people. Chechen rebels were blamed again.
Medvedev has called on his government to do "everything in order for the criminals who committed this crime to be established, found and brought to justice. And the nest where these bandits are hiding, whatever their name is, should be exterminated."
CNN's Maxim Tkachenko and Ivan Watson contributed to this report
