India said today it was not considering military action against Pakistan in response to last week's terror attacks on Mumbai as the United States and its allies rushed to mediate between the two nuclear-armed neighbours.

Pakistan also tried to ease the tension with its historic nemesis by offering a joint investigation into the attacks ahead of a visit by Condoleezza Rice, the US Secretary of State, to India tomorrow.

However, India's Hindu nationalist opposition kept up the pressure on the Government to find a robust response to the assault on Mumbai, which is being blamed on the Pakistan-based militant group, Lashkar-e-Taiba (LeT).

LeT was also blamed for an attack on the Indian Parliament in 2001, which prompted India and Pakistan to mass troops on each other's border, almost triggering the two countries' fourth war since independence in 1947.

Pranab Mukherjee, the Foreign Minister, said there would be no such response this time, seeking to reassure Western officials anxious about the knock-on effects on military operations against Islamist militants in Pakistan and Afghanistan.

"Nobody is talking about military action," he told reporters. Instead, India demanded last night that Pakistan take "strong action" against militants on its soil and extradite 20 fugitives including Dawood Ibrahim, a Mumbai mafia don thought to have links to LeT.

Pakistan, which banned LeT in 2002, has denied any role in the Mumbai attacks and offered to cooperate in India's investigation, although it retracted an earlier offer to send its intelligence chief to Delhi.

Shah Mehmood Qureshi, Pakistan's Foreign Minister, said in a televised address today that now was not the time for a "blame game, taunts, finger-pointing".

"The government of Pakistan has offered a joint investigating mechanism and a joint commission to India. We are ready to jointly go into the depth of this issue and we are ready to compose a team that could help you," he said. "Pakistan wants good relations with India."

However, he did not respond to India's request to extradite Ibrahim and the others, including Hafiz Mohammad Saeed, the LeT founder, and Maulana Masood Azhar, the head of the militant group Jaish-e-Mohammad (JeM).

Pakistan has said in the past that it will not hand over any of its citizens to India and denies that Ibrahim, an Indian national, is on its soil.

Pakistan has also warned that if India massed troops on its border, it would respond by diverting troops fighting al-Qaeda and Taleban militants in its northwestern tribal areas near the Afghan border.

Air Chief Marshall Jock Stirrup, Britain's chief of defence staff, said that such a move would undermine the progress that Pakistan had made against the militants in recent months.

"If tensions between India and Pakistan continue to escalate, there's a risk they and we could be diverted from the real issue: dealing with the terrorist groups who perpetrate such criminal and barbaric acts," he said in a speech.

"Nothing would warm the terrorists' hearts more than knowing that they'd succeeded in setting state against state."

President Bush has demonstrated his concern about that prospect by ordering Ms Rice to interrupt a visit to Europe and fly to Delhi to meet Indian leaders tomorrow.

She met David Miliband, the Foreign Secretary, in London and both said they expected Pakistan to cooperate with India's investigation, a view echoed by EU foreign policy chief Javier Solana.

Tomorrow, she is expected to urge India to maintain its current restraint despite mounting political pressure to make a robust response ahead of national elections, due by May.

"We welcome the fact that the Indian government has been pretty restrained so far," one Western diplomat told The Times. "That helps with our objective to get India and Pakistan to talk to each other."

Meanwhile, the main opposition Bharatiya Janata Party (BJP) stepped up its efforts to exploit public outrage at the government's failure to prevent the Mumbai attacks.

The BJP, which was in power when India and Pakistan almost went to war in 2002, stopped short of calling for military action – but only just.

Arun Jaitley, the BJP General Secretary, compared the Mumbai attacks to the 9/11 attacks on the United States.

"Our response must be close to what the American response was," he said. "This time Pakistan is not entitled to be given the benefit of the doubt."

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