EU-China relations have soured over a number of disputes, including security concerns about Chinese telecom giant Huawei and China's national security law on Hong Kong, which complicated investment treaty negotiations.
"It is important also to continue understanding the origins of the pandemic and therefore we were very clear that it is very important to give World Health Organization all the possibilities to lead its investigations on the origin of Covid-19", von der Leyen said.
"The EU and our member states have responded with one clear voice - democratic voices in Hong Kong should be heard, rights protected, and autonomy preserved", Mr Michel said.
Speaking at a virtual summit on Monday, Xi called for a peaceful coexistence, mutual cooperation and multilateralism between China and its largest trading partner, the EU. In the first eight months, a total of 7,601 China-Europe freight train trips were made, up by 44 percent over the same period in 2019.
The EU also wants stronger commitments on climate change from China, the world's top polluter. China is working toward the goal of fostering a new, dual-cycle development architecture with the domestic cycle as the mainstay and with domestic and global development reinforcing each other.
As an important economy and the largest single market in the world, the European Union has been China's largest trading partner for a long time, said Feng Zhongping, vice president of the China Institute of Contemporary International Relations (CICIR). "We need China to move".
However, she emphasised that "there is still a lot that remains to be done in other important and hard chapters of the agreement, particularly in two areas: market access and sustainable development".
At this drastic moment, China and the European Union, which account for about a quarter of the world's population and one third of gross global product, need to step up efforts to advance cooperation and strengthen coordination to better handle challenges in a post-pandemic era.
"We as Europeans act in close cooperation - we offer our global partners respect, and we expect the exact same from them", Maas said.
Despite the pandemic, economic and trade cooperation between the two sides remain robust in 2020.
Xi urged actively carrying out tripartite cooperation with Africa on the basis of full respect for African countries' will, calling on the worldwide community, especially multilateral financial institutions and commercial creditors, to take stronger actions on debt relief in Africa.
Turning to human rights issues, Michel said the three had a "quite intense discussion" with Xi, notably on China's restive far western province of Xinjiang, where authorities have cracked down on local Uighurs.
Chinese people will not accept "an instructor" on human rights and oppose "double standards".
In an interview with Xinhua ahead of a China-Germany-EU leaders' meeting, Gu Xuewu, director of the Center for Global Studies at Germany's University of Bonn, said that the European political circles attach great importance to the meeting because it is expected to provide guidelines for future EU-China ties. "Now Europe's interest is just flagging".
Furthermore, the two sides should work together to crack open new areas for cooperation, as Xi proposed at the 22nd China-EU leaders' meeting in June, to forge a green and digital partnership between China and the EU by fostering cooperation in clean energy, sustainable finance, e-commerce and cloud computing.
The European Commission has been negotiating with China on an investment agreement for more than six years.
In the field of the economy and trade, the cornerstone of China-EU relations, Beijing and Brussels share a promising future. Xi pushed back against what he described as meddling in China's internal affairs, saying the country wouldn't expect outside parties to act as an "instructor" on human rights.
The leaders also exchanged views on global and regional issues including the Afghanistan and the Iranian nuclear issues, agreeing to strengthen communication and coordination and to make joint efforts in maintaining worldwide and regional security and stability.