The two leaders, who will be present in Ufa to attend the SCO summit, will be meeting on the sidelines of it.
Modi enquired about Sharif, his mother and family.
This will be the fourth visit of Modi to China after he came to power in 2014.
Jammat-ud-Dawah chief and Mumbai attack mastermind Hafiz Saeed on Tuesday warned Pakistan Prime Minister Nawaz Sharif against extending a hand of friendship to India.
China on Monday said India's membership bid in the NSG has become "more complicated" under the "new circumstances" as it again ruled out backing New Delhi's entry in the grouping, saying there should be non-discriminatory solution applicable to all non-NPT signatory countries.
Prime Minister Narendra Modi on Wednesday gifted Kazakh President Nursultan Nazarbayev a set of books relating to religions born in India.
India requested Pakistan to let Modi's aircraft fly over its airspace when he travels to Bishkek. Pakistan accorded an "in principle" approval to India's request.
There is a possibility of a meeting between Prime Minister Narendra Modi and his Pakistani counterpart Nawaz Sharif on the sidelines of the annual summit of Shanghai Cooperation Organization in Russia.
An MoU on sharing hydrological information of the Brahmaputra River by China to India and another pact on amendment of the protocol on phytosanitary requirements for exporting rice from India to China to include non-Basmati rice were signed after the Modi-Xi talks in the eastern Chinese port city.
At the conference, they were seated across the horse-shoe-shaped table.
'Problems will keep recurring unless China vows to resolve all outstanding issues between the two sides,' says Sana Hashmi.
'If an 'informal meeting' with Xi Jinping materialises before the SCO summit in June, that itself could be regarded as a significant breakthrough in India-China relations,' says Ambassador M K Bhadrakumar.
With Shanghai Cooperation Organisation set to admit India and Pakistan amid growing rancour over their Nuclear Supplies Group membership bid, a Chinese state-run daily expressed concern on Friday that the hostility between them may have a "negative effect" on the security grouping.
It seems China is ready to cooperate with India in the central Asian region through the SCO framework, the reasons for which are manifold, says Sana Hashmi.
The civilian leadership informed the military authorities that Sharif's hour-long meeting with Jindal was a part of back-channel diplomacy. And Jindal had the backing of some important Indian officials for the meeting to defuse ongoing tension between the two countries, the report said.
He said countries should work for promoting open and inclusive cooperation for win-win outcomes.
However, there will be no bilateral meetings between Swaraj, Sitharaman with their Pakistani counterparts.
We have seen great strides in all-around cooperation, Chinese foreign ministry spokesperson said.
India is likely to send a high-level delegation, headed by the minister, given the conference's importance.
The telephonic talk between Modi and Xi came a day after Modi congratulated Xi on Chinese social media.
China continued to stonewall India's entry harping on the need to have a criterion for countries like India which have not signed the Nuclear non-Proliferation Treaty and clubbing India's case with that of Pakistan for which it is batting.
The meeting on the sidelines of the Shanghai Cooperation Organisation Summit in Bishkek is their first interaction after Modi's re-election following the stunning victory of the BJP in the general elections last month.
India says it cannot accept a project that ignores its core concerns on sovereignty and territorial integrity.
The summit is being seen as an effort by India and China to rebuild trust and improve ties that were hit by the 73-day-long Doklam standoff last year among other contentious issues.
The entire gamut of China's activities is aimed at keeping India on tenterhooks, cause fatigue to its troops and keeping its security system unstable, so that it cannot play a meaningful role in international geopolitics as an effective partner of the US and Japan, observes Lieutenant General Syed Ata Hasnain (retd).
Amid escalating tensions at the Indo-Pak border, Pakistan's national security advisor Sartaj Aziz has said it is "too early" to speculate on the timing of his visit to New Delhi to hold talks with his Indian counterpart as agreed at Ufa.
India, which has an Observer status for the past 10 years, will technically become the member by next year.
"The Prime Minister thanked the Prime Minister of Pakistan for his telephone call and greetings," MEA said.
India on Friday sought resolute and comprehensive global action against terror infrastructure, saying the challenge must be taken seriously as different "theatres" are getting interconnected through terror networks as well as globalisation of the "supply chain of ideology".
The meeting, which lasted for nearly 50-minutes, comes in the backdrop of stiff Chinese opposition to India's entry into the NSG, which looks after critical issues relating to nuclear sector, including trade and export of nuclear technology.
Parrying a direct reply on whether there will be a meeting between Khurshid and Aziz on the sidelines of Shanghai Cooperation Organisation meet, Spokesperson in External Affairs Ministry said the External Affairs Minister will take the opportunity to interact "informally" with several other leaders present there.
'Beijing is comfortable with Hasina's pragmatism -- perceived as 'pro-India', but staying out of Indian orbit and receptive to forging close ties with China and yet, siding with neither neighbour,' says Ambassador M K Bhadrakumar.
Prime Minister Narendra Modi on Saturday termed terrorism and climate change as the biggest problems faced by the world saying the solutions to these can be found in Mahatma Gandhi's life and ideals.
India is expected to have a bigger say in pressing for concerted action in dealing with terrorism as well as on issues relating to security and defence in the region.
Though the "eye of the storm" is away from land, the cyclone's outer periphery would leave its impact on the coast.
China on Monday said differences remain among members of the Nuclear Suppliers Group over the inclusion of new countries and the issue was not even on the agenda of the grouping's meeting in Seoul this week, a day after External Affairs Minister Sushma Swaraj asserted that Beijing was not opposing India's entry
On the sidelines of the SCO visit in Ufa, the two heads met and decided to revive dialogue and find ways to expedite the trial of the Mumbai attacks.
'Lingering border disputes and fierce geostrategic competition in South Asia between China and India are likely to temper any cooperation Beijing might hope to achieve with New Delhi in the SCO,' says P K Vasudeva.
The summit is being seen as an effort by India and China to rebuild trust and improve ties that were hit by the 73-day-long Doklam standoff last year.
'The new order cometh, sweeping out the old,' notes Ambassador B S Prakash.
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