Neave Barker, Al Jazeera's correspondent in Moscow, said many people in the capital were "still nervous about venturing underground".
"The Kremlin is now under mounting public pressure to review its security policy," he said.
Medvedev's predecessor, Vladimir Putin, who is now prime minister, has also vowed that those responsible for the attacks would be "destroyed".
The death toll from the bombings rose on Tuesday to 39 after a young woman died in hospital, a Russian health official said.
Andrei Seltsovsky, the chief of Moscow's health department, said 71 other people were still in hospital, five of them in critical condition.
Putin, who cut short a visit to Siberia to return to Moscow, said "a crime that is terrible in its consequences and heinous in its manner has been committed".
"I am confident that law enforcement bodies will spare no effort to track down and punish the criminals. The terrorists will be destroyed," he said before visiting survivors in hospital.
Caucasus rebels blamed
No group has claimed responsibility for the bombings, but Russian authorities, who have blamed separatist fighters from the North Caucasus region for previous attacks, once again pointed the finger at the region's fighters.
Barker said Russian intelligence services remain convinced that two female suicide bombers with links to separatist fighters were responsible.
"Even before the death toll became official yesterday, the head of the intelligence service already made it very clear that they felt the links were obvious, this after only a few months the main line between Moscow and St. Petersburg was targeted by attackers," he said.
Officials said the attacks, at Lubyanka in the city centre and Park Kultury in the southwest, were carried out by two women wearing belts packed with the explosive hexogen and metal shrapnel.
"Body parts of two terrorists - female suicide bombers - were found at the scenes of the blasts," Alexander Bortnikov, the chief of Russia's Federal Security Service (FSB), said in a televised meeting at the Kremlin.
The headquarters of the FSB, the successor to the Soviet-era KGB, is located just above Lubyanka station.
"According to preliminary information, these people had links to places of residence in the Northern Caucasus," Bortnikov said.
Sergei Lavrov, Russia's foreign minister, said foreign involvement in the attacks had not been ruled out.
|Security camera at Park Kultury metro station showing casualties after the blast [Reuters]
"We all know very well that clandestine terrorists are very active on the border between Afghanistan and Pakistan," the Interfax news agency quoted him as saying at a Group of Eight ministers' meeting in Canada.
"We know that several attacks have been prepared there, to be carried out not only in Afghanistan, but also in other countries.
"Sometimes, these journeys go as far as the Caucasus," he said, although he did not offer any evidence or explain the links.
Russian police are searching for two women who accompanied the suspected suicide bombers, plus a man who may also have been an accomplice, after identifying them and the suspected bombers through surveillance footage, Interfax reported, citing a security source.
Our correspondent said the bombings have "to be seen as a politically motivated attack targeting what is perhaps one of the most symbolic signs of Russian authority in the capital".
In February, Doku Umarov, the leader of a Chechen separatist group, said in an interview on a rebel-affiliated website that "the zone of military operations will be extended to the territory of Russia".
Umarov, who claimed responsibility for the bombing of a passenger train travelling between Moscow and St Petersburg in November, warned that "the war is coming to their cities".
Russian forces fought two wars with Chechen separatists, and last year declared that the conflict was over.
However, the violence has spread from Chechnya to the neighbouring regions of Dagestan and Ingushetia.