At a press conference on his return from a foreign trip which also took him to Islamabad and India, the UN chief also called for resumption of Indo-Pakistan dialogue to resolve all outstanding questions, including Kashmir.
Responding to a question about the tensions between India and Pakistan, he said that he had impressed upon the Pakistani leaders, including President Asif Ali Zardari and Prime Minister Yousuf Raza Gilani, that they should fully cooperate with India and thoroughly investigate the Mumbai attacks.
Ban Ki-moon said the Pakistani leaders had "committed to me" that they will "fully cooperate" with India in the probe.
"During my visit to India and Pakistan, I was reasonably relived and also gratified that leaders of both countries are committed to cooperating" to resolve the issue, he added.
Prime Minister Gilani, he said, had told him that Pakistan was in the process of enacting a legislation by which the government can punish those who commit crimes outside their territory. "That is very commendable," he added.
Asked about the Kashmir issue, Ban said the relationship between the two countries was so important for the subcontinent and the region that all the pending issues should be resolved through composite dialogue they had initiated.
The world leaders, including himself, had urged leaders of both countries to calm down at a time when the relations between them were "very tense" after the Mumbai attacks. They had appealed to them to resolve the issue through bilateral talks.
In his opening remarks, the secretary-general also formally announced that the three-member United Nations Commission to look into the assassination of former Pakistani Prime Minister Benazir Bhutto will be headed by Chile's U.N. Ambassador Heraldo Munoz.
Meanwhile, officials said the composition of the commission was yet to be finalized. It includes Indonesia's former Attorney General Marzuki Dar Usman will be a member of the commission, but no decision has been made on its third member. He or she will be either from Sweden or Norway, they said.
Ms. Bhutto was killed in a gun and suicide bomb attack on Dec. 27, 2007, as she left an election rally in Rawalpindi.