The news was welcomed by India as a "positive development", but Foreign Minister Pranab Mukherjee said Pakistan still needed to crack down on militant camps.
"We will share whatever (information) we can. We expect that Pakistan would take credible steps to dismantle the infrastructure which are used by these terror elements," Mukherjee told reporters.
Mukherjee is slated to make a detailed statement in parliament later on Friday.
India's main Hindu nationalist opposition, the Bharatiya Janata Party (BJP), said Pakistan had finally emerged from its denial mode.
"With this revelation, now the next stage should be eliminating the terrorist camps inside Pakistan and crushing the association between state actors and these terrorist groups," BJP spokesman Rajiv Pratap Rudy said.
Indian newspapers welcomed Islamabad's acknowledgement of Pakistani involvement in the Mumbai attack.
"Pak blinks, finally," read the headline in the Times of India newspaper, while the Mail Today led a story with "Finally, Pakistan admits some guilt".
Pakistani officials shared the findings of the investigation with India's High Commissioner Satyabrata Pal on Thursday, giving details of how 10 gunmen had sailed from Karachi to carry out the attack that killed 179 people in the Indian financial capital between November 26-29.
Tensions have been running high between India and Pakistan since the attack, though fear of a conflict between the nuclear-armed neighbours has receded in recent weeks.
India has maintained the plot was hatched in Pakistan, and the slow speed with which Islamabad has acted fuelled Indian suspicions that Pakistani intelligence agencies have not cut their old ties with jihadi groups.
Analysts said Pakistan's announcement had assuaged much of India's mounting frustration.
"Now we have to see how effectively they can conduct the judicial process," said strategic analyst Uday Bhaskar.
Analysts said Pakistan's move had come not only because international pressure had come to a boil, but also because of growing disquiet within its civil society.
"Is this the beginning of the mea culpa within the Pakistan establishment about terrorist acts being directed against India?" said Bhaskar.
"We will have to wait and see how Pakistan handles its right wing. Nonetheless this admission itself is also very important."