Anders Fogh Rasmussen, the Nato secretary-general, who argued at the weekend for the West to embrace Russia as a partner for global security, said the alliance "remains committed to co-operating with Russia in the fight against international terrorism".
Herman Van Rompuy, the president of the 27-member European Union, also sent Medvedev a message of solidarity and condolences, as did Angela Merkel, Germany's chancellor, who expressed "shock and horror", her spokesman said.
Nicolas Sarkozy, the French president, likened the bombings to the September 11 attacks on the US and said Russia deserved the support of all democracies.
"When New York was attacked, all the world's democracies were attacked. And when Moscow is attacked, we are all attacked," he said during a trip to New York.
International police agency Interpol has also extended its help to Russia to track down the plotters behind what it called "despicable and senseless attacks".
Jean-Michel Louboutin, the executive director of Interpol, said: "[We have] offered every support and made available all of [our] resources to the Russian authorities in their investigation into these attacks".
Other leaders who strongly condemned the attacks include Hu Jintao, the Chinese president, who said China "supported Russian efforts to strike down terrorism", and Gordon Brown, the British prime minister, who said he was "appalled" and that there "will never be any justification for acts such as these".