"There must be a response for the sustainment of the regime," Nixey said, alluding to Putin's strongman image and previous promises of stamping out the militancy in Chechnya.
Putin led Russia into its second post-Soviet war against rebels in the North Caucasus province of Chechnya after a series of deadly apartment building bombings in Moscow and other cities.
Putin at one point vowed that rebels would be tracked down and killed even "in the outhouse," typical of the tough talk that bolstered his popularity during his 2000-2008 presidency.
"This is a direct affront to Vladimir Putin, whose entire rise to power was built on his pledge to crush the enemies of Russia," Jonathan Eyal of Britain's Royal United Services Institute said of the bombings.
President Obama condemned the attacks, saying the "American people stand united with the people of Russia in opposition to violent extremism and heinous terrorist attacks that demonstrate such disregard for human life."
President Medvedev said the government would act "without compromise" against terrorism. "We shall continue operations against terrorists without wavering and to the end."
In response to the attacks, Russia's civil aviation authorities have ordered all local airports to increase security, a spokesman for the authorities told Reuters.
The NYPD told ABC News today that it " is increasing police coverage of the New York City subway system as a precaution" after the Moscow bombings.
No group has yet claimed responsibility for the attack, which is the worst attack to hit the Russian capital since February 2004, when a suicide bombing on the subway killed at least 39 people.
Many Muscovites fear a return of the Black Widows, the name given to a group of female suicide bombers from Chechnya.
They first appeared during the Moscow theatre hostage crisis in 2002. Dressed from head to toe in black they sought revenge for the loss of their male relatives killed by the Russian military in Chechnya.
Also dubbed the Brides of Allah these female suicide bombers have struck in Moscow before with devastating effect.
In August 2004 a woman detonated herself outside a metro station, killing 10 and in July 2003 two female suicide bombers hit a concert killing at least 15. Also in 2004 female suicide bombers set off explosives on two passenger jets.
In November last year, a bombing on the Nevsky Express north of Moscow, killed 26 people. An Islamist separatist group from the North Caucasus claimed responsibility for that attack.
Both stations hit today are now open. A fast clean up job has removed the blood and debris but the walls are scarred with shrapnel marks.
Passengers entering them were fearful.
"It's really terrifying," said Vasily Vlastinin, 16. "It's become dangerous to ride the metro, but I'll keep taking the metro. You have to get to school, to college, to work somehow."
Mark Crudele and Reuters contributed to the reporting of this story.