Monday's bombings were the first to hit Tashkent since an alleged 1999 assassination attempt on the president.
Reports said a police officer was also killed in a subsequent shoot-out with suspects.
"In total, including the Bukhara incident, 19 people are dead, including six police officers", Prosecutor General Rashid Kadyrov told reporters at a press conference in Tashkent.
Foreign Ministry spokesman Ilkhom Zakirov earlier said officials were not sure whether the explosion at an apartment block in the Silk Road city of Bukhara, was related or an accident. It was unclear whether anyone was hurt or killed in that blast.
Zakirov said arrests have been made and an investigation is under way, blaming the blasts on "terrorists."
The government had been scheduled to make a televised statement about the attack, but by mid-afternoon state-run TV still hadn't reported on the explosions. Other bazaars and shops were closed across the city.
Russia's ITAR-Tass news agency reported that according to initial information, a woman had blown herself up.
At least one blast occurred around 9am (04:00 GMT) at the Chorsu market in the Old City, said Alimzhon Turdakulov, spokesman for the National Security Service.
Uzbek President Islam Karimov
was targeted in 1999
It was believed to have struck near the entrance to a children's store. Russia's Echo of Moscow radio, citing the RIA-Novosti news agency, said several people had been killed.
Officials at the Interior Ministry refused to comment.
Zakirov tied the explosions with the recent train bombings in Madrid and with continuing turbulence in neighbouring Afghanistan.
A series of near-simultaneous bombings in Tashkent in February 1999 were blamed on the Islamic Movement of Uzbekistan, which has been linked to the al-Qaida network.
Uzbek authorities said the blasts, which killed 16 people, were an attempt to assassinate Karimov.
Uzbekistan became a key ally of the United States after it
opened up its main military base for use in the US-led campaign in Afghanistan following the September 11 attacks in 2001.