Mohammed Ajmal Amir Qasab faces a string of charges
Pakistan's parliament has urged India to respond positively to offers from Islamabad to help in the investigation into the Mumbai (Bombay) attacks.
In a resolution, the National Assembly also condemned what it called "war hype" between the two neighbours.
Indo-Pakistani relations have been badly strained since the attacks, in which more than 170 people were killed.
India says Pakistani militants carried out the attacks. Pakistan denies any involvement.
Earlier on Wednesday police said Mohammed Ajmal Amir Qasab, the sole surviving suspect from the attacks, was again remanded in custody, this time until 6 January.
War 'not an option'
Pakistani political parties made a rare show of unity shortly after last month's attacks, when they said they shared India's grief but rejected "hasty allegations" against their country.
Since then, relations have spiralled downwards and India has put peace moves on hold.
Delhi wants decisive steps taken against militants operating from Pakistan. The government in Islamabad says it has yet to be given solid evidence upon which to act.
On Wednesday, the National Assembly called upon India to respond to what it called "constructive proposals" made by the Pakistani government.
The assembly highlighted joint investigations and "high-level engagement" aimed at "addressing concerns relating to the Mumbai incident".
MPs also urged India to exercise restraint.
"[The house] condemns the war hype in a situation where war is not an option given the nuclear capabilities of both countries," the assembly said.
Although tensions have risen in recent weeks, few observers believe the countries are likely to go to war.
The multiple attacks on the city on 26 November left at least 173 people dead, including nine of the 10 gunmen.
TEN NAMED GUNMEN
Nasir, alias Abu Umar (Nariman House)
Abu Ali (Taj Palace)
Soheb (Taj Palace)
Fahad Ullah (Oberoi)
Mohammed Ajmal Amir Qasab(survived)
Bada Abdul Rehaman (above left, Taj Palace)
Abdul Rehaman Chota (above right, Oberoi)
Ismal Khan (CST station)
Babar Imaran (Nariman House)
Nazir, alias Abu Omer (Taj Palace)
Mohammed Ajmal Amir Qasab, who has previously been identified also as Mohammed Ajmal Qasab and Azam Amir Qasab, faces a number of charges including murder, attempted murder, waging war against a country and criminal conspiracy.
He had been due to appear in court, but because of security concerns magistrates and court officials visited him at the Mumbai police crime branch office.
Mumbai crime branch chief Rakesh Maria said the extension of Mr Qasab's custody "has been taken in the case of hijacking a car on the day of the Mumbai attacks".
Police say Mohammed Ajmal Amir Qasab and his accomplice Ismal Khan opened fire indiscriminately at Mumbai's CST station and two other places, where they killed more than 50 people, including three top police officers.
Ismal Khan was shot dead but Mohammed Ajmal Amir Qasab was taken alive and has been undergoing "sustained interrogation" since then, police say.
He was remanded into custody on 27 November, a day after his arrest. His custody was extended for a further two weeks on 11 December.
Under Indian law police are required to file charges within 90 days of arrest. But correspondents say that it could take longer in the case of Mr Qasab because he is accused of 12 different offences.
Indian lawyers have so far refused to defend him.
However, anyone accused of a crime is entitled to legal aid in India and this would have to be provided when the accused asks for it before the court.
On Monday, India handed a letter to Pakistan it says was written by Mr Qasab, confirming he is Pakistani and asking for Islamabad's help.
The Pakistani authorities have yet to respond officially to the letter.
Indian officials say evidence gathered from the bodies of the dead gunmen and the boats in which they travelled to Mumbai indicated they were Pakistani nationals belonging to the militant group, Lashkar-e-Taiba.