Asif Ali Zardari also vowed to crack down on anyone involved in the attacks who was residing in Pakistan, saying a raid Sunday on a training camp run by the banned Lashkar-e-Toiba group was evidence of his resolve.
"Pakistan is committed to the pursuit, arrest, trial and punishment of anyone involved in these heinous attacks," he wrote in an opinion piece for The New York Times.
Sunday's raid in Pakistani Kashmir was Islamabad's first reported response to intense Indian and US demands for it to act against alleged perpetrators of the Mumbai attacks on its soil.
Zaki-ur-Rehman Lakhvi, who India has said was a mastermind of the assaults, and several other members of the militant group Lashkar-e-Toiba were arrested, an intelligence official and a senior government official said on condition of anonymity because of the sensitivity of the information.
The government has not officially released the names of those it is holding.
Late Monday, the military said it has begun "intelligence-led" operations against banned groups like Lashkar, but gave no more details.
Analysts say Lashkar-e-Toiba was created in the 1980s by Pakistan's intelligence agencies to act as a proxy fighting force in Indian Kashmir. India accuses it in the Mumbai attacks.
India and Pakistan have fought three wars since 1947, but ties between the nuclear-armed neighbors had been improving in recent years and a slow-moving peace process was under way.
US officials fear a serious disruption in relations would dent its hopes for regional stability needed to better fight al-Qaeda along the Afghan border.
"To foil the designs of the terrorists, the two great nations of Pakistan and India ... must continue to move forward with the peace process," Zardari wrote.
Analysts have said the peace process would likely be halted for several months or longer due to tensions triggered by the attacks, but no one on either side had formally suggested abandoning the negotiations.
Many experts suspect elements within Pakistan's intelligence agencies keep some links with Lashkar and other militants, either to use them against India or in neighboring Afghanistan, but US counterterrorism officials say there is no evidence linking Pakistan state agencies to the Mumbai attacks.
Indian officials say the sole Mumbai attacker captured alive has told them that Lakhvi recruited him for the mission and that Lakhvi and another militant, Yusuf Muzammil, planned the operation.
India has not commented on his reported arrest. State Department spokesman Sean McCormack did not confirm it, but said raid was a "positive step."
The United States says Lashkar is linked to al-Qaeda. In May, the US blocked the assets of Lakhvi and three other alleged members of the group, including its leader, Hafiz Mohammed Saeed.
Pakistan banned the group in 2002 following US pressure, but there have been few if any convictions of its members. An Islamist charity called Jemaat-ud-Dawa sprang up after the ban, which US officials say is a front for the group.
Jemaat-ud-Dawa — which denies any link to Lashkar — runs a chain of schools and clinics throughout the country and has helped survivors of two deadly earthquakes in recent years.
Moving against that network amid pressure from the US and traditional rival India risks igniting Muslim anger that could destabilize the county's shaky, secular government.
Two of Pakistan's wars with India were fought over Kashmir. In 2001, an attack by suspected Lashkar-e-Toiba militants on the parliament building in New Delhi brought the countries close to a fourth conflict.
The Mumbai attacks came as India was preparing for national elections in spring. Opposition parties, including the hard-line Hindu nationalist Bharatiya Janata Party, hope to make gains amid anger at alleged security lapses before the attacks.
But the ruling Congress party won two state elections Monday, including in the capital New Delhi, and was leading in a third, election officials said, in an early sign that opposition charges were not sticking.