Islamabad denies any involvement, but India's Deputy Home Minister Shakeel Ahmad told the BBC it was "very clearly established" that all the attackers had been from Pakistan.
Indian Minister of State of External Affairs Anand Sharma described the attacks as a "grave setback" to the normalisation of relations with Pakistan.
Meanwhile, US Secretary of State Condoleezza Rice urged Pakistan to co-operate.
"I don't want to jump to any conclusions myself on this, but I do think that this is a time for complete, absolute, total transparency and cooperation and that is what we expect," she said during a visit to London.
Mr Deshmukh told a press conference on Monday: "I have offered to resign. If the responsibility of the attacks is on the chief minister, then I will go."
Suspect named as Azam Amir Qasab
21 years old, fluent English speaker
Told police he is from Faridkot village, in Pakistan's Punjab province
Said the attackers took orders from handlers in Pakistan
Home Minister Shivraj Patil resigned on Sunday, saying he took "moral responsibility".
His successor, Finance Minister Palaniappan Chidambaram, said he was "disinclined" to take the post but had done so to "answer the call of duty".
The BBC's David Loyn in Delhi says the resignations are not likely to be the last, with public anger now of a different order to what it has been during previous terrorist incidents.
Our correspondent says the latest revelation, in police reports, that personal belongings of 15 men were found aboard an abandoned ship from which the attacks were launched has raised questions as to whether all the gunmen have been found.
Only 10 militants have been identified, one of them captured alive. Quoted by a private TV channel, survivor Azam Amir Qasab apparently confirmed that there were 15 attackers.
HOW THE ATTACKS HAPPENED
Militants take over trawler at sea, then sail into Mumbai on inflatable dinghies
Militants head to attack locations in four groups by taxi
First attack on railway terminus
More attacks follow on a cafe, two luxury hotels and a Jewish centre
Questions have been asked about India's failure to pre-empt the attacks, and the time taken to eliminate the gunmen.
A report in the Hindustani Times newspaper said a militant from the Pakistan-based group Lashkar-e-Toiba arrested and questioned in February told intelligence services he had inspected the five-star Taj Mahal Palace and Oberoi-Trident hotels, which were among targets attacked last week, and several other buildings in December 2007.
Quoted by his interrogator, the militant said he had passed on information to the group's operational commander. Lashkar-e-Toiba has denied involvement in the attacks.
Also, Reuters news agency quoted Damodar Tandel, head of Maharashtra's main fishermen's union, as saying he had warned the government about attempts to bring RDX explosives to Mumbai by sea but no-one acted on the information.
I looked back to see the waiter who was serving me getting hit by a bullet
The violence which began on Wednesday night finally ended on Saturday morning, when Indian troops killed the last of the gunmen at the Taj Mahal Palace hotel.
"I have gone by my conscience and put in my papers," Maharashtra Deputy Chief Minister RR Patil was quoted by news agency Press Trust of India as saying.
Public anger has been building up against Mr Patil ever since media reports that he made light of the terror attack by saying that such "minor incidents do happen in big cities".
On Sunday, Prime Minister Singh held a cross-party meeting in Delhi.
Indian prime minister on anti-terror plans
Mr Singh was quoted by Reuters news agency as saying he planned to increase the size and strength of the country's anti-terrorist forces.
While the vast majority of victims were Indians, at least 22 foreigners are known to have died, including victims from Israel, the US, Germany, Japan, Canada, Australia, Italy, Singapore, Thailand and France. One Briton, Andreas Liveras, was also killed.
Hundreds of people took to the streets of Mumbai on Sunday to protest at the perceived government failures.
Police continued on Sunday to sift through the debris in the Taj hotel.
They are also questioning the one attacker who was captured alive to try to establish who masterminded the assault.
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