They said evidence from the interrogation of Azam Amir Kasav, the only gunmen of the 10 not killed by commandos, clearly showed that Pakistani militants had a hand in the attack.
The clean-shaven 21-year-old with fluent English was photographed during the attack wearing a black t-shirt emblazoned with the Versace logo.
He is reported to have said his team took orders from what he described as the command in Pakistan.
A police officer told journalists the training was organised by the Lashkar-e-Taiba militant group, and conducted by a former member of the Pakistani army.
New Delhi has not accused Islamabad's civilian government of involvement but has expressed deep frustration that its neighbour has been unable or unwilling to prevent militants using its soil to attack Indian cities.
Pakistan President Asif Ali Zardari has appealed to India not to punish his country for last week's attacks, saying militants could precipitate a war.
In an apparent attempt to deflect the blame, intelligence agencies told TV channels they had repeatedly warned of an imminent attack on Mumbai by sea. But police and coastguard officials denied receiving any actionable intelligence.
The chief minister of Maharashtra state, of which Mumbai is the capital, has offered to resign. Vilasrao Deshmukh, a member of the ruling Congress party, could follow his his deputy, state home affairs minister R R Patil.
Indian national Home Affairs Minister Shivraj Patil also stepped down yesterday, as Prime Minister Manmohan Singh said he would overhaul and boost the nation's counter-terrorism capabilities.
Mumbai residents returned to schools and offices on Monday for the first time since the attacks.
Timeline of Mumbai attacks
The Mumbai assaults by Islamist militants is said to bear the hallmarks of Lashkar-e-Taiba, a Pakistan-based group blamed for attacks in India including a 2001 parliament blast that almost plunged the two countries into a fourth war.
US Secretary of State Condoleezza Rice has urged Pakistan to give its total cooperation in finding the perpetrators of the attacks.
Ms Rice said this was the time for complete, absolute and total transparency. She will visit India on Wednesday.
Candlelight vigils were held in New Delhi and at various spots in Mumbai last night.
Candles, flowers and pictures were also strewn at the bullet-scarred Cafe Leopold and at the barricades in front of the Taj and Trident hotels, where the gunmen holed themselves up during the 60-hour siege.
More vigils and remembrances were planned in the city, with messages going out as mass texts, e-mails and Facebook messages.
