Russian President Vladimir Putin ordered the state security services, the FSB, to launch an investigation.
There was speculation Chechen rebels were behind the attack, ahead of presidential elections in the republic on Sunday – but this has been denied by rebel leaders.
A spokesman from Moscow’s Domodedovo airport said no foreigners were on either passenger list.
Security has been tightened at Russian airports.
When told of the two crashes, Russia’s UN ambassador, Andrey Denisov, said: “Now we have to see if there’s terrorism,” reported the Associated Press news agency.