Gilani travelled to Sharif's country estate Raiwind in Punjab province for a two-hour-long luncheon meeting after which the prime minister said his Pakistan People's Party and the PML-N should "remove misunderstandings" and work together for the sake of democracy and economic development in Pakistan.
"Today I have come on behalf of the federal government, offering an olive branch to Mian Nawaz Sharif. I have come on behalf of my party and on behalf of President Zardari" who has sent a message of goodwill, Gilani told media persons after the meeting with the two-time premier.
The meeting is their first after Zardari capitulated to lawyers protests on March 16 when the government acceded to PML-N demand to reinstate Chaudhry and other judges sacked by ex-President Pervez Musharraf during the 2007 emergency.
Sharif demanded that the ruling PPP take steps to scrap the president's sweeping powers and to restore the constitution to its status before a military takeover in 1999.
"Gilani sahab is our prime minister and (PPP chief Asif Ali) Zardari sahab is our president. If the Charter of Democracy is implemented, there is no question of us going towards any destabilisation," he said.
More than 16 months after he was removed unceremoniously for not endorsing the emergency rule, 60-year-old Chaudhry formally "assumed charge of the office" in Islamabad after midnight on Saturday night following retirement of Abdul Hamid Dogar, said a release issued by the supreme court of Pakistan.
Gilani also said the possibility of the PPP and PML-N working together could not be ruled out if the apex court reversed its verdict disqualifying the Sharif brothers from electoral politics.
Using cricket language, Sharif said," They (PPP) have won the toss and started their innings. They are batting and we are bowling. It should be a good match so the people of Pakistan can enjoy it and be happy."
Sharif said a key demand of the PML-N was fulfilled with the government's decision last week to reinstate the deposed judges.
The PPP-led government should now implement the Charter of Democracy, which was signed by the two parties in 2006, Sharif told a joint news conference with Gilani.
Under the provisions of the Charter of Democracy, the 17th constitutional amendment that gives the President sweeping powers should be scrapped and the constitution restored to its original position to ensure justice and rule of law, Sharif said.
Sharif made it clear that the two parties had not held any discussions on the PML-N rejoining the PPP-led government at the centre.
Hundreds of lawyers and activists who have agitated for Chaudhry's return gathered outside the judge's home in Islamabad for a ceremonial flag-raising. They carried balloons and threw rose petals, calling the judge's reinstatement a milestone for democracy.
"It is a day of victory for the people of Pakistan,'' lawyer leader Aitzaz Ahsan said.