The government has not responded to the report but President Asif Ali Zardari told U.S. President George W. Bush that anyone found involved in the attack on India's financial hub in which 179 people were killed would be dealt with.
India has blamed the assault on the Pakistan-based Islamist group Lashkar-e-Taiba (LeT).
It was set up by Pakistani security agencies in the late 1980s to fight Indian rule in the disputed Kashmir region but officially banned in 2002, after Pakistan signed up to the U.S.-led campaign against terrorism.
The Wall Street Journal said in an online report at least one top LeT leader, Zarar Shah, captured in an early December raid in Pakistani-controlled Kashmir, had confessed to the group's involvement in the attack.
"He is singing," an unidentified Pakistani security official told the newspaper.
India's angry accusation of a Pakistani link to the assault on Mumbai has revived old hostilities between the nuclear-armed rivals and raised fears of conflict.
Pakistan has condemned the Mumbai attacks and has denied any state role, blaming "non-state actors," and has promised to prosecute anyone found linked to the attack. But it has ruled out sending Pakistanis to India for trial.
Zardari reiterated to Bush that Pakistan would not allow its territory to be used for launching attacks on other countries, Zardari's office said. Bush had called Zardari, it said.
"Anyone found involved in such attacks from the soil of Pakistan would be dealt with sternly," Zardari told Bush.
The Wall Street Journal, citing the Pakistani security official, said Shah's admission was backed up by U.S. intercepts of a telephone call he had with one of the attackers during the assault.
Shah told interrogators that he was one of the main planners and he had spoken to the attackers during the rampage to give them advice and keep them focused, the newspaper cited a second person familiar with the investigation as saying.
Shah had implicated other LeT members, and had broadly confirmed the account the sole captured gunman told Indian investigators, the newspaper cited its source as saying.
According to Indian reports, the captured gunman told Indian interrogators the 10 attackers trained in Pakistani Kashmir and later went by boat from Karachi to Mumbai.
India's home minister, P. Chidambaram, repeated India's line that its neighbor must act on what India says is evidence of Pakistani militants' involvement.
Pakistan has repeatedly said India has not provided evidence.
"If anyone is in a state of denial anything that we give will be denied," Chidambaram told reporters in New Delhi, referring to a statement from the surviving gunman captured in Mumbai.
Shah was picked up with another LeT commander, Zaki-ur-Rehman Lakhvi, in raids on militants launched after the attack, Prime Minister Yousaf Raza Gilani told reporters on December 10.
Pakistani authorities did not have evidence that the LeT was involved in the attacks before the militants were arrested in Kashmir. Their arrest was based on guidance from U.S. and British authorities, the newspaper cited an official as saying.
Pakistan and India have fought three wars since independence from Britain in 1947 and came to the brink of a fourth after gunmen attacked the Indian parliament in December 2001.
India has put a "pause" on a five-year-old peace process that had brought warmer ties.
(Additional reporting by Kamran Haider and Krittivas Mukherjee; Writing by Robert Birsel; Editing by Charles Dick)
(For a Reuters blog about Pakistan please see http://blogs.reuters.com/pakistan )