The president said his country's investigators would look into Indian claims that Pakistanis were involved in the terrorist attacks in Mumbai last week, which left at least 171 people dead.
"If we had proof, we would try them in our courts. We would try them in our land and we would sentence them," Zardari said in a TV interview on Tuesday evening.
On Monday, India sent an official note to Pakistan's ambassador in New Delhi demanding the extradition of 20 people believed to be involved in terrorist activities. The Indian government says the 10 terrorists, who travelled to Mumbai by sea from Karachi, had been trained in Pakistan.
Indian investigators said the only terrorist captured alive, 21-year-old Azam Amir Kasav, confessed to having received arms training in Pakistan.
Indian Foreign Minister Pranab Mukerjee said on Tuesday that New Delhi has handed over extensive evidence that the horrific attacks were orchestrated in Pakistan.
However, the Pakistani leader said: "So far this is just a list of names. There are no clues, no investigation, we have received nothing."
The list of suspects that India is attempting have extradited has not been officially released. However, an Indian TV channel cited government officials as saying the list includes organized crime boss Dawood Ibrahim, and Masood Azhar, head of the south Asian militant group Jaish-e-Mohammad.
In the 1980s, Dawood Ibrahim headed one of the most powerful criminal groups in Mumbai (then Bombay), and is believed to have organized a series of bombings in the city in 1993, an apparent revenge for the destruction of the Babri masjeed mosque by Hindu fanatics. More than 250 people were killed and hundreds more injured in the attack.
Indian investigators suggest that Ibrahim aided terrorists from a group called "Lashkar-e-Taiba" (Army of the Righteous) in their attack last week.
Masood Azhar has already served time in an Indian prison for his participation in a terrorist group. However, he was freed in exchange for the release of hostages on a hijacked India Airlines passenger plane in 1999. Azhar is based in Pakistan, where he founded his group Jaish-e-Mohammad (Army of Mohammad). He is the main suspect in organizing an attack on the Indian parliament in 2001.
Although India put Ibrahim and Azhar on an international wanted list long ago, they remain free, and Pakistan officially denies that they are residing in the country.
After last week's terrorist attacks in India, Pakistan's government has sent its condolences and promised to cooperate. Both countries have agreed to meet in India with Pakistan's intergovernmental investigations officials to exchange information on the investigation of the terrorist acts.
Indian suspicions of Pakistani involvement in the attacks have inflamed relations between the two nuclear-armed countries, which have in the past fought three wars.
