The president of the former Soviet republic, the autocratic Islam Karimov, a one-time Communist party boss, said the explosions were an attempt on his life.
One blast was inside government headquarters where Mr Karimov was to address the cabinet yesterday morning.
A policemen said he heard gunfire and grenade concussions as the president's car approached the cabinet building. The city centre was sealed off by armed police and troops and Russian television showed several wrecked vehicles next to deep craters, and tall buildings with shattered windows.
Shortly after the bombs - a rare outbreak of political violence in this country of 22 million - President Karimov, 61, said on state television the attackers aimed to "sow fear and panic in the civil population".
The president, nicknamed "Papa" by his subjects, has not shortage of enemies. Aided by his ruthless security forces, he has crushed almost all opposition in the last seven years.
He was first elected in 1991 in a poll widely seen as suspect and he extended his term in office by a referendum in 1995.
Two suspects were held at Tashkent airport in the afternoon, said Russian commentators. Speculation is likely to focus on an Islamic connection. Secular Uzbekistan has long feared the rise of Islamic fundamentalism, imported from neighbouring Afghanistan, Pakistan and Iran, ignited by the religious freedom and dire social conditions resulting from Soviet collapse.
Tensions have also sharply increased with next-door Tajikistan, which has accused Tashkent of fuelling its civil war by helping the anti- government forces.
And Uzbekistan, irked by what it saw as domineering Russian tactics, recently announced its withdrawal from a security co-operation treaty between the 12-member Commonwealth of Independent States.
Yesterday, the Kremlin moved quickly to condemn the attack, issuing a statement from President Boris Yeltsin, who called it a "cynical terrorist act".Reuse content