The two leaders have met twice after their informal summit in the Chinese city of Wuhan.
Prime Minister Narendra Modi and Chinese President Xi Jinping have concurred that there had been a "perceptible improvement" in bilateral ties after their Wuhan summit and both sides are optimistic that 2019 would be an even better year for India-China relations.
During their fourth meeting this year, PM Modi and Chinese President Xi on Friday discussed joint efforts to further enhance mutual trust and friendship between the two giant neighbours during their meeting on the sidelines of the G-20 summit in the capital of Argentina.
The two leaders have met twice after their informal summit in the Chinese city of Wuhan in late April — once at the Shanghai Cooperation Organisation (SCO) summit held in June in China's Qingdao and the second time at the BRICS summit in South Africa's Johannesburg in July.
"Had a wonderful meeting with President Xi Jinping," Prime Minister Modi tweeted about his meeting and said the talks revolved around a wide range of bilateral and global subjects.
"Our regular interactions have added significant strength to India-China ties," he said.
Asserting that their Wuhan informal meeting was a milestone in the Sino-India ties, PM Modi told Chinese President Xi that he was looking forward to host him for an informal summit next year.
"Such initiatives are helpful in maintaining the momentum," PM Modi said, adding that there "have been two review meetings — in Qingdao and in Johannesburg".
He said the ties between the two countries have made huge strides over the last one year.
The relations between the two neighbours were strained last year following a 73-day standoff in Doklam in the Sikkim sector of the border.
The chill between the two sides later improved resulting in an informal summit between PM Modi and Chinese President Xi at Wuhan where the two leaders decided to issue "strategic guidance" to their militaries to strengthen communications to build trust and understanding, a move aimed at avoiding a Doklam-like situation in the future.
PM Modi said Friday's meeting will strengthen further the partnership between the two nations. "Today's meeting will be important in providing a direction in terms of strengthening our relations," he said.
"I express my heartiest thanks to you (President Xi) for taking out time for this meeting," he said.
Later, Foreign Secretary Vijay Gokhale told reporters that the two leaders said that there had been a perceptible improvement in bilateral relations.
"Both of them had a very detailed review of what they agreed to in Wuhan and how it was progressed. Both of them said that progress has been made on the economic side," he said.
President Xi referred to enhanced imports of rice and sugar from India, spoke of possibility of greater import of soyameal and rapeseed. He also expressed the hope that India would import more agricultural products from China, Mr Gokhale said.
The president also indicated that in the pharmaceutical sector there would be greater trade between the two sides, he said.
"On the political side, they welcomed the visit of the Chinese defense minister, of the holding of the counter-terrorism military exercise next week in India and the recently concluded special representative talks.
"Both leaders (said) that there had been a positive improvement in border management along the India-China border areas following the Wuhan summit," the foreign secretary said.
PM Modi and Chinese President Xi also said they were looking forward to the first meeting of the high-level mechanism on people-to-people exchanges in New Delhi in December.
"Both sides also specifically mentioned that the first bilateral cooperation that had begun in Afghanistan which is the training of Afghan diplomats, had been successful and that they were looking for further such opportunities," Mr Gokhale said.
"Both leaders felt that as a result of the Wuhan Summit and the meetings taking place after that, strategic communication had been enhanced between them, trust had been built between them. There was a personal relationship and both sides were optimistic that 2018 was a good year but 2019 would be an even better year," the foreign secretary said, describing the meeting as "very successful".
During the meeting, Chinese President Xi told PM Modi that many important consensus reached on the development of China-India relations are being implemented and the ties are steadily improving, according to a statement issued by the Chinese Foreign Ministry in Beijing.
Referring to the talks between the Special Representatives on the boundary as well as defence and various other delegations, he said the two sides should work together to build an open world economy and make globalisation more open, inclusive, balanced and beneficial to all, it said.
"We should oppose protectionism and unilateralism, uphold the core values and basic principles of the World Trade Organisation (WTO)," Chinese President Xi said.
His call for joint action came ahead of his meeting with US President Donald Trump, who has asked China to cut down the USD 375 billion trade deficit in their bilateral trade and slapped additional tariffs on over USD 250 billion Chinese exports to US. China too retaliated sparking a trade war between the two countries.
Chinese President Xi said it is necessary for India and China to deepen pragmatic cooperation, expand bilateral trade, strengthen cooperation in investment, medical and health, poverty reduction, environmental protection, disaster prevention and reduction, and expand people-to-people and cultural exchanges.