At least 19 people have been killed and 26 others injured in a series of blasts and attacks in Uzbekistan.
Karimov urged Uzbeks to "unite like a fist against... evil attempts"
Prosecutor General Rashid Kadyrov said suicide bombers killed three policemen and a child in an attack at a bazaar in the capital, Tashkent.
There were also three fatal shootings of policemen in Tashkent, and a blast at the home of an alleged extremist in Bukhara, that killed 10 people.
Uzbekistan's president linked foreign extremists to the attacks.
In a televised address to the nation, President Islam Karimov stressed his view that whoever was responsible must have connections with a foreign organisation.
Officials said two of the blasts - in Tashkent's crowded Chorsu bazaar were carried out by women suicide bombers operating for the first time in Central Asia.
"These were terrorist acts," Mr Kadyrov told reporters at a news conference in Tashkent, blaming religious extremists.
"There is reason to believe they were prepared over a long period and co-ordinated from a centre, possibly abroad," he said.
Foreign Minister Sadyk Safayev said the attacks were aimed at undermining the US-led coalition against terrorism, in which Uzbekistan has been a staunch ally of Washington.
Police said they had found radical Muslim literature among explosives at one of the crime scenes, however no-one has so far claimed the responsibility for the attacks.
The BBC's Monica Whitlock in Tashkent the alternative view is that Uzbek militants are adopting a new way of striking at old targets - in this case the police.
The police - who wield great power in Uzbekistan - are widely seen as instruments of the state rather than defenders of the law.
'Hands of international terror'
The bombs at the Chorsu bazaar exploded at about 0900 (0400 GMT). One of the female suicide bombers blew herself at a nearby police rally ground, while the other set off the bomb at a bus stop.
In separate incidents late on Sunday and early on Monday, three police officers were killed in shootouts with gunmen in and around the capital, Mr Kadyrov said.
The Bukhara explosion happened at an alleged bomb-making factory, he added.
Mr Kadyrov described the attacks and what he called global terrorism as "links in the same chain", our correspondent says.
On his part, Mr Safayev said the attacks were carried out by "the hands of international terror, including Hizb ut-Tahrir and Wahhabis".
Hizb ut-Tahrir, which aims to set up a pan-Islamic state that would include post-Soviet Central Asia, and the Wahhabi school of Sunni Islam are both outlawed in Uzbekistan.
Immediately after the attacks, Uzbek security forces carried out vehicle checks throughout the capital to prevent possible suspects from fleeing.
Security has been stepped up across the capital
Uzbekistan's neighbours have also been quick to react by strengthening border security and increasing inspections at checkpoints.
Our correspondent says the unrest in Uzbekistan is a signal of the true feelings in the strictly-controlled state - that while on the surface everything seems calm and placid, there is a violent undercurrent.
There are Islamic groups who may resent Uzbekistan's support for the US in the war on terror, and there are groups who want to be able to trade freely and resent the extortion payments some police demand, our correspondent says.
Now that anger is bubbling to the surface, our correspondent adds.