The two leaders, who arrived almost at the same time here last evening for attending the BRICS summit, engaged shortly thereafter for what was described as "good discussions and good meeting".
The meeting was scheduled for 40 minutes but it went on for 80 as it was freewheeling discussion without any constraints.
The two leaders appeared well prepared for the meeting as both of them referred to the statements made by the other before they assumed power, Akbaruddin said.
He quoted Xi as saying that "when India and China meet the world watches us".
President Xi in particular referred to Modi's experience in Gujarat as Chief Minister and his focus on development.
The discussions centred around all aspects of the bilateral relations, regional and international matters, he said.
The surprise invitation for the APEC summit as part of partnership and engagement came in the context of the two leaders discussing the need for the two countries to work together in international fora like BRICS and other fora.
Today's meeting was the fourth high-level engagement between the two countries since the Modi government assumed charge six weeks ago.
First Xi's emissary Wang came to Delhi, followed by the visits of Vice President Hamid Ansari' and Army Chief Gen Bikram Singh to China recently.
Xi acknowledged his visit to India in September and extended an invitation to Modi to visit China, which was accepted.
The dates will be decided by diplomatic channels, he said.
Asked if India has accepted the invitation for the APEC summit, Akbaruddin said November was a busy month with SAARC and G 20 meetings scheduled but New Delhi considers the invitation as a significant gesture which will be given very serious consideration.
Xi also told Modi that India should work more deeply with the Shanghai Cooperation Organisation but the prime minister pointed out that New Delhi was only an observer. If other members were willing, India was ready to work with SCO more closely.
On the boundary question, Modi said there was need for finding a solution and maintenance of peace and tranquillity on the border was essential for resolving the issue.
It was a substantive and a very cordial and warm meeting in which the two leaders struck a personal rapport which augurs well for the future, the spokesman said.
He said the prime minister emphasised that there should be no incidents on the border that would undermine the bilateral relations.
To a question on the incursions by the Chinese army on the border, Akbaruddin said India conveyed its concerns to China on the issue.
On his part, Modi also emphasised on the economic relations between the two countries and talked about cooperation in the infrastructure sector, industrial parks and investment.
He referred to the adverse trade imbalance against India and sought correction of the situation.
Xi acknowledged that there was a possibility of enhanced trade, particularly in the services sector from the Indian side and the increased Chinese tourist numbers to India.
Modi referred to the visit of Chinese travellers coming to Gujarat in the ancient period.
The possibility of additional Mansarovar yatra route was raised by Modi considering the fact that he had himself undertaken that pilgrimage in difficult conditions in the present route.
Xi gave an assurance that China will consider the request for the additional route.
Both the leaders touched on the historic and civilisational links between the two countries, especially the Buddhist links.
The Prime Minister referred to terrorism and extremism and said India and China should work together to fight the menace in the region in view of the common civilisational heritage they had.
Replying to questions whether any timeliness were discussed on resolving the border question, Akbaruddin said obviously since it was a first meeting between them they could not go beyond their initial references and stated positions.