"Our investigation into the Mumbai attacks is continuing," Zardari said in an interview to The Independent.
"Some of these terrorists may in fact have been born in Pakistan. But we believe that this operation was international, with significant support from within India itself," he said when asked whether Pakistan had any news about the nine militants whose bodies are still in a mortuary in Mumbai.
Asked to comment on India's charge that Pakistan was not doing enough to assist in the investigation into the Mumbai attacks, Zardari said, "I think the Indian government is not dissatisfied with the level of our cooperation."
"We have offered to help, and we have helped. We have made substantial arrests of people within groups that may have been involved in the Mumbai attacks," he said.
"But we need cooperation from India to build the case for effective prosecution of these accused in our courts. Many of the extremists are the same people that conduct acts of terrorism within our own country," Zardari said.
He noted that Pakistan had condemned the Mumbai attack on November 26 last year.
"Mumbai was attacked and we condemn it. But let us remember that every day Pakistan is attacked by terrorists. They destroyed our Marriott hotel in Islamabad and killed over 50 people," Zardari said.
"We will co-operate with all nations including our neighbours in identifying and pursuing terrorists wherever and whoever they are. We will prosecute them and we will punish them upon conviction." the president said.
"Remember, this is our war. Our children and women are dying, and hundreds of our soldiers have been killed," the Pakistan President noted, referring to the frequent suicide bombings and terror attacks in the country, especially in the restive tribal areas bordering Afghanistan.
"Pakistan above all nations on earth is in the trenches of the war against these fanatics and terrorists. Our very existence is at stake," Zardari added.