The meeting is being held in Dubai as Pakistan People's Party co-chairman Asif Ali Zardari had gone there to meet his family.
A Pakistan Muslim League (Nawaz) team led by its president Shahbaz Sharif travelled to Dubai on Monday night for parleys. Serious differences emerged over the reinstatement of the judges, especially after the PPP linked the issue to a package of constitutional reforms which it says is aimed at ensuring the independence of the judiciary and preventing its misuse by military dictators.
"We don't consider the existing set-up in the Supreme Court to be constitutional. It's as simple as that," Shahbaz Sharif told reporters in Dubai shortly after his arrival with senior PML-N leaders and federal Ministers Khwaja Asif and Chaudhry Nisar Ali Khan.
Shahbaz said his party wants the National Assembly to pass a resolution restoring the judges, following which they would be reinstated through an executive order issued by the prime minister.
PPP leader and Law Minister Farooq Naek is also in Dubai to assist Zardari in the talks.
Before leaving for Dubai, Naek denied the impression that Zardari was opposed to the restoration of the judges. He said Zardari only wanted the restoration to be done "without any clash".
The National Assembly or lower house of parliament is likely to be convened on April 30 if the PPP and PML-N resolve their differences and agree on the resolution for restoring the judges.
The PML-N and PPP signed an agreement in March to restore judges who were sacked for not endorsing last year's emergency rule, within 30 days of coming to power.
However, Zardari has been non-committal on meeting this deadline. PML-N chief Nawaz Sharif has said the restoration of the judges cannot be linked to any such package and insisted that the judges be reinstated by April 30.
The influential legal fraternity which is spearheading a movement for restoring the judiciary, has warned that lawyers will organise nationwide protests if the judges are not reinstated by the end of April.
Reports have also suggested that the PPP has reservations over reinstating deposed Supreme Court Chief Justice Iftikhar Muhammad Chaudhry, with Zardari himself saying that his party believes in strengthening the judiciary and is not keen on taking up the cases of individual judges.
Sharif and the lawyers' movement, however, have said they will not accept any restoration of the judiciary that excludes Chaudhry. Senior PML-N leader Javed Hashmi has even warned that ministers from his party will resign if the deadline to restore the judges is not met.
The PML-N has drawn consolation from Prime Minister Yousuf Raza Gillani's statement that all the deposed judges, including former Chief Justice Chaudhry, will soon be restored.
PML-N joint secretary Siddique-ul-Farooq told PTI that "90 per cent of the problems facing Pakistan" will be overcome if the judges are restored as the move will ensure the balance of power between the executive and the legislature. He said the credibility of any party opposing the restoration of the judges would be "compromised in the eyes of the nation".