Witnesses said four armed militants entered a house, which was then surrounded by the security forces.
An interior ministry statement read out on television said 20 militants blew themselves up with home-made explosives after being surrounded. Three policemen were killed and five were injured.
At least five bodies were reported to be lying in the street.
"You just can't imagine how terrible it was," one resident, 76-year-old Lyudmila Petrovna, told Reuters.
"First the special forces turned up like a bolt from the blue, all wearing masks and armed to the teeth.
"Then we were hastily evacuated and - along with our relatives - heard explosions and the shooting."
The interior ministry said a number of different operations were taking place in parts of the city, but gave no details.
The authorities have blamed Islamic extremists for the attacks which are the bloodiest seen in the former Soviet republic for five years.
The violence began on Sunday evening with an explosion at a house used by alleged militants in Bukhara, the authorities said.
"The explosions in Tashkent could be revenge for Uzbekistan's housing U.S. military bases in support for the operation in Afghanistan," the Russian business daily Kommersant said in a commentary.
The IMU is believed to have been seriously weakened by the U.S.-led operations in Afghanistan and allegedly received new blows recently in the Pakistani military's hunt for terrorists near frontier with Afghanistan.
Andrei Kokoshin, the head of a parliamentary committee in charge of Russia's relations with other ex-Soviet republics, said the latest violence could be linked to the fighting in Pakistan earlier this month in which many IMU members were reportedly captured.
"It could be that these actions accompanied a demand for their release," Kokoshin said on Echo of Moscow radio.
Arkady Dubnov, a columnist for the daily Vremya Novostei and an expert on Central Asia, said that by targeting police, the organizers of the latest violence could have sought to win over the population.
Malashenko said the terrorists could have targeted the authorities simply because they were driven into a corner.
While the insurgents have utilized some terrorist techniques, in particular suicide bombings, some observers in Tashkent believe the attacks may not be connected to known Islamic radical groups, such as Hizb and the Islamic Movement of Uzbekistan. Instead, it may be the work of a new group, with its origins rooted in the despair generated by the Karimov government’s stranglehold over the country’s political and economic life.
Karimov in a televised address March 29 claimed that Islamic radicals, in concert with international terrorist groups, had been planning the attacks for up to eight months. However, some eyewitness accounts raise doubts about assertions of an international connection. First, some reports indicate that the insurgents were poorly armed. The account that some insurgents took pistols from police officers would appear to substantiate these reports. At the same time, the bombs employed by the insurgents appear to be crudely fashioned, with limited explosive force, assembled with locally available components. Some observers feel that if either the Hizb or the IMU had been involved in the attacks, the insurgents would have been better equipped.
Virtually everyone interviewed over the past two days expressed little sympathy for the police, and said government policies were driving people to revolt. A man interviewed near the TTZ tractor plant vented about the complete lack of civil rights and economic opportunity in Uzbekistan. The attacks, the man asserted, are a "serious expression of popular anger."
"There may be more incidents tomorrow and the day after tomorrow, and into the future because people are desperate," said the man, who like all those interviewed refused to give his name, citing concern about government retribution. "Until the situation concerning human rights and the economy is resolved, the source of terrorism will not be rooted out."