Umarov is the self-proclaimed leader of the "Caucasus Emirate", a separatist group that seeks to free the mainly Muslim North Caucasus from Moscow's rule.
Last Friday's attack against the luxury Nevsky Express train, running between Moscow and St Petersburg, was the worst attack in Russia outside the North Caucasus in five years.
The statement on KavkazCenter.com said the train "was mainly used by Russia's leading officials".
At least two government officials were killed in the train bombing, and Alexander Bastrykin, chief of Russia's Investigative Committee, was injured by a remote-controlled blast when he arrived at the scene the next day.
Chechen rebels have previously issued other claims that have turned out to be false, including one for an August disaster at a Siberian hydro-electric power plant that was later shown to have been caused by a technical fault.
Neave Barker, Al Jazeera's correspondent in Moscow, said if the rebels' claims are true "it could force the Kremlin to take a much tougher stance on separatist activity in the Caucasus", which "had, until now remained largely contained".
"And with the Caucasian Mujahideen promising more attacks, the authorities are under mounting pressure to protect the Russian people," he said.
Russian prosecutors have opened an investigation into the rail disaster, which has raised fears of a new wave of attacks in major Russian cities.
The country has not experienced a major attack in its heartland since a spate of suicide bombings in Moscow in 2003 and 2004.
However violence in the North Caucasus region is seen on an almost daily basis, where fighting between rebels and local authorities continues following two brutal wars in Chechnya.
Earlier this week three suspected rebels were killed and six police officers wounded in clashes in Chechnya and Dagestan.
Rights groups have said that arbitrary arrests, torture and extrajudicial killings by security forces have fueled violence in the region.