Ms Swaraj, the Indian foreign minister, described peace and tranquility on the countries' border areas as an "essential prerequisite for the smooth development of bilateral relations".
Swaraj was received by Deputy Foreign Minister of Mongolia B Battsetseg.
Whether or not China will be able to win India round to the Belt and Road will likely be a key measure of the success of Prime Minister Narendra Modi's trip to China to meet Xi for an informal meeting on Friday and Saturday.
Defence Minister Nirmala Sitharaman also landed in Beijing earlier on Tuesday to attend preparatory meetings with the External Affairs Minister on the sidelines of the SCO meeting.
There are a number of challenges that are being faced by the world today, foremost being the threat of global terrorism and the imminent need to build a strong security architecture to combat it, the minister said.
Last week, the SCMP reports, after meeting Nepal's Foreign Minister Pradeep Kumar Gyawali, Wang floated the idea of a trilateral economic corridor with India and Nepal as part of its trade initiative.
Xi and PM Modi met last September and are scheduled to meet again in June for the Shanghai Cooperation Organization meeting in China's eastern port city of Qingdao.
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Swaraj said India wants to "strengthen cooperation within the SCO framework for comprehensive, cooperative and sustainable security". Differences persist over the border issue, China's growing military assertiveness in the Indo-Pacific region, and Beijing's mollycoddling of Islamabad despite Pakistani terrorism against India.
"We should also urgently resolve to establish Comprehensive Convention on International Terrorism that India proposed more than two decades ago in the United Nations".
The meeting ended with an announcement of informal Summit, Resumption of Kailash Mansarowar Yatra through Nathu La route, resumption of data sharing for Sutlej & Brahmputra rivers, and active participation at SCO Foreign Ministers Meeting.
In doing so, she said, India will continue to be guided by the requirements of the government of Afghanistan and the shared objectives of the global community.
"India is committed to working with SCO to strengthen our economic and investment ties". All other ministers showed support.
Against that backdrop, former Indian foreign secretary S. Jaishankar told India's Asian News International that the summit was "certainly a very bold step".