Kayani made the suggestion when he called on PML-N chief Nawaz Sharif, set to become prime minister for a record third term following his party's victory in the May 11 polls, at his brother Shahbaz Sharif's home in Lahore on Saturday.
The News daily quoted its sources as saying that Kayani wanted the new government to take gradual initiatives with utmost caution to improve relations with India as this alone "may lead to lasting peace in the region".
Kayani ensured that Sharif "knew the exact situation on the ground with regard to Pakistan-India ties in the backdrop of developments over the last decade" as Sharif did not have first-hand experience in view of his absence from power, the report said.
In Kayani's view, the relationship between Pakistan and India "demands a comprehensive strategy for addressing the geopolitical challenges which have cropped up over the years" since Sharif's last tenure as premier.
There was no official word from the PML-N or the army on the meeting.
Before the elections, Sharif had made some surprisingly positive statements on ties with India which many thought may not have gone down well with the army, the News said.
The PML-N chief had said he is keen on resuming the India-Pakistan peace process that was interrupted in 1999 by then army chief Pervez Musharraf, who ousted Sharif's government in a military coup.
The report said Kayani called on Sharif to congratulate him on the PML-N's success in the general election and informally talked "about all national security issues".
He informed Sharif that the new premier and his cabinet would be given a briefing on all important internal and external national security challenges after their swearing-in.
The armed forces are "fully behind the democratic government and had worked hard for ensuring democracy", Kayani was quoted as saying.
Kayani reportedly stressed the need to bring the armed forces and the government on the same page as the towering challenges facing Pakistan required "symphonic harmony between the two important pillars of the state".
He also discussed the situation in Afghanistan and the challenges awaiting the new government for negotiations on this issue.
The army chief reportedly said the pull-out of the US and its allies from Afghanistan in 2014 would "surely have an impact on the new government" and Pakistan should prepare for this significant development in advance, especially handling "affairs at the time of the US withdrawal and afterwards".
Speaking on internal threats, Kayani reportedly said he believed terrorism was a serious issue which needs to be "handled with care by evolving complete harmony among all the federating units".
He maintained it would largely depend on the federal government and how far it would go to develop solid relations with all provinces despite the split mandate.
Kayani further said the situation in Khyber-Pakhtunkhwa, Balochistan and Karachi require a great deal of attention and a sincere attempt is imperative to defuse tension at all levels.
For this, a concerted effort is the need of the hour, and all institution need to have complete mutual understanding for resolving all pending issues, he reportedly said.
Apart from the government, all major players will have to cooperate to achieve internal peace, Kayani was quoted as saying.
Sharif reportedly assured the army chief that the PML-N government would leave no stone unturned to address pressing issues facing the country.
He said the government would work hand-in-hand with all state institutions.
All key issues will be discussed in parliament, and all stakeholders taken on board in making important decisions.
Another report in The News quoted an unnamed top military official as saying that the meeting would go a long way in ensuring smooth functioning of the democratic system with complete focus on the domestic and regional security situation.
The official said the meeting was arranged to "prevent any suspicions and doubts in any quarter that there was any threat to democracy or the newly elected leadership".
The meeting can be seen as a confidence-building measure to ensure there is no tension and clash of institutions, especially after Sharif's statements that the army chief would not get any further extensions and his desire to improve relations with India, the official said.
Kayani reportedly did not raise the issue of his extension but "there was a lingering feeling in the meeting that the vast experience and hands-on knowledge of handling critical matters for years must be put to some use", the report said.
Photograph: Faisal Mahmood/Reuters
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