Sayed Zabiuddin, an Indian-born member of the Lashkar-e-Taiba, was detained at Delhi international airport on June 21 when he arrived from the Middle East.
Zabiuddin "had found a very safe haven in Pakistan," Chidambaram told reporters.
"Pakistan should admit that (he) did go to Pakistan, that he was part of the group which prepared Kasab and nine others, that (he) was in the control room among one of the handlers and masterminds of the attack.
"Just as we admit facts, Pakistan should also admit facts," the minister said.
Indian police say Zabiuddin, who also goes under the names Abu Hamza and Abu Jundal, has confessed to being a key handler for the 10 militants who attacked India's financial capital in 2008, killing 166 people.
According to police, he admitted being present in the "control room" in Karachi from where the attack was monitored and coordinated.
Pakistan has asked India to share information on Zabiuddin and urged New Delhi to refrain from blaming Islamabad.
"India should supply details... enabling us to take action," Pakistan's advisor on interior affairs, Rehman Malik, said Wednesday.
"Let us end the blame game... We have to fight terrorism together," Malik added.
Pakistan has indicted seven people for their alleged role in the Mumbai attacks but their trial, which began in 2009, has been beset by delays.
The United States has offered a $10 million reward for information leading to the conviction of Lashkar founder Hafiz Saeed who lives openly in Pakistan and is accused of masterminding the attacks.
Ajmal Kasab, the lone surviving gunman from the attack, is currently on death row in a Mumbai prison.
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