"On Security Council, China also took note of our aspirations. For the first time it is reflected in the document," Jaishankar told reporters.
The statement was made following talks between Indian Prime Minister Narendra Modi and his Chinese counterpart Li Keqiang in Beijing.
According to the countries' joint statement made during Modi's visit to Beijing, "China attaches great importance to India's status in international affairs as a large developing country."
The two sides agreed on the need for comprehensive UN reform and stressed the importance of the increased participation of developing countries in UN affairs and governance structures, so as to make the body more effective.
The parties also agreed to strengthen mutual trust and manage their differences, as well as to continue seeking a "reasonable and mutually acceptable" solution to the border dispute in the Himalayas. India considers parts of the border area to be part of its northwestern state of Kashmir, but the territory has been administered by China since the 1962 Sino-Indian war.
The nations also contest part of India's Arunachal Pradesh state, considered to form part of China's Tibet by Beijing.
Indian Prime Minister Modi began his three-day visit to China on Thursday. He met his Chinese counterpart Xi Jinping in Shaanxi province before heading to Beijing and Shanghai in a bid to boost bilateral economic cooperation.