Shivraj Patil, India's home minister, has already stepped down – the first political casualty of the attacks - with analysts warning of more resignations in the coming days.
Manmohan Singh, the prime minister, has said that martime and air security will be strenghtened, with the elite National Security Guard receiving four new regional hubs, including Mumbai.
The ruling Congress Party will have one eye on General Elections due next year and therefore will want to be seen to be acting swifty and strongly.
Meanwhile, the death toll from the attacks - that began on Wednesday and lasted for 60 hours - has been revised down to 172 from initial estimates of 200 dead. More than 200 others were injured in the three-day seige.
Residents of Mumbai began to return to normal life on Monday, with schools and businesses re-opening and traffic once again clogging up the streets.
Rice in diplomatic push
Also on Monday, the authorities finished removing bodies from the Taj Mahal hotel.
The hotel is the last of the siege sites to be cleared by security forces who completed their search for bodies and booby traps on Monday.
In other developments, Condoleeza Rice, the US secretary of state, announced she would be visiting New Delhi on Wednesday to discuss security threats in the wake of the attacks.
The talks are expected to centre on how to defuse rising tensions between India and neighbouring Pakistan following the massacre.
New Delhi has continued to link those behind the attacks to Pakistan and said on Sunday that they were raising security to a "war level".
However, Islamabad strongly denies any connection to the massacre.
'Don't punish Pakistan'
Asif Ali Zardari, the Pakistani president, urged India not to punish his country or allow "non-state actors" to push the two states to war, in an interview published on Monday in the UK-based Financial Times newspaper.
Zardari underlined the battle against extremists was a joint one: "Even if the militants are linked to Lashkar-e-Taiba [a Pakistan-linked Islamist group], who do you think we are fighting?"
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Deshmukh, chief minister of Maharashtra, offered his resignation on Monday [EPA]
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"We live in troubled times where non-state actors have taken us to war before, whether it is the case of those who perpetrated [the] 9/11 [terror attacks on the US] or contributed to the escalation of the situation in Iraq," he said.
"The architects of this calamity in Mumbai have managed to raise a threat on our other (Indian) border. As we have these people on the run along our western border (with Afghanistan), our attention is being diverted at this critical time," Zardari told the Financial Times.
Some Indian security experts rejected the threat.
"It's part of the usual blackmail of the United States that Pakistan does to take more interest in India-Pakistan issues," said B. Raman, a former head of Indian intelligence agency RAW.
"They think this kind of argument will make the United States sit up and take notice of their sensitivities and do something about it," he added, referring to warming ties between Washington and New Delhi, including a nuclear accord.
Rice has been in contact with both countries' foreign ministers over the last few days in an attempt to maintain diplomatic relations between the two states.
With the suspicion that "elements" in Pakistan were involved, the Indian government is considering suspending peace talks with Islamabad, the Press Trust of India (PTI) news agency reported on Monday.
Although the Indian government confirmed it has moved troops to the Line of Control at the quasi-border with Pakistan in disputed Kashmir, it maintains that the ceasefire is still in place.
A man, who police say is the sole attacker captured alive after the siege, said he belonged to a Pakistani armed group with links to the disputed Himalayan region of Kashmir, a senior police officer said on Sunday.
Joint Police Commissioner Rakesh Maria said Ajmal Qasab told police he was trained at a Lashkar-e-Taiba camp in Pakistan, the group that was, he said, "behind the terrorist acts" in Mumbai.
A US counter-terrorism official said some "signatures of the attack" were consistent with Lashkar and Jaish-e-Mohammed, another group that has operated in Kashmir. Both are said to have links with al-Qaeda.