European Commission President Ursula von der Leyen and European Council President Charles Michel had video calls with Chinese Premier Li Keqiang and President Xi Jinping, where they discussed ties, as well as China's security law for Hong Kong.
The European Union has told China to make good on a promise to open up its economy and warned of "very negative consequences" if Beijing goes ahead with a new security law on Hong Kong that the West says will curtail basic rights.
Speaking after video calls with Chinese Premier Li Keqiang and President Xi Jinping, the EU's chief executive and chairman said they had repeated accusations that Beijing has spread disinformation about the coronavirus.
"The relationship between the EU and China is simultaneously one of the most strategically important and one of the most challenging that we have," European Commission President Ursula von der Leyen told a news conference on Monday.
European Council President Charles Michel said China was not reciprocating the welcome that Chinese companies receive in Europe.
Calling China a partner and a rival, von der Leyen said Beijing had not followed up on a 2019 deal to allow greater access for European companies in China or drop rules requiring investors to share their know-how in Chinese joint ventures.
Even before the coronavirus pandemic worsened Sino-European ties, the EU found itself caught between China and the United States, needing both and reluctant to alienate either.
Li expressed optimism about the relationship, according to Chinese state media, saying China and the EU are more partners than competitors.
But the EU wants to see progress on an investment agreement under negotiation since 2014.
EU officials say they want to see movement in areas such as autos, biotech and micro-electronics and see Beijing limit subsidies for state-run companies.
Germany has postponed an EU leaders' summit with Xi in September, citing the coronavirus, though diplomats said it was in part because of the impasse in investment negotiations.
Controversial Hong Kong law
Michel and von der Leyen said they told Li and Xi of their concerns over China's security law for Hong Kong, which democracy activists, diplomats and some businesses say will jeopardise its semi-autonomous status and role as a global financial hub.
China's Parliament reacted angrily on Saturday to a resolution by the EU assembly protesting against the security law.
"We also conveyed that China risks very negative consequences if it goes forward with imposing this law," von der Leyen said, without giving details.
"The European Union is in touch with our G7 partners on this topic and we've made our position very clear to the Chinese leadership today and urged them to reconsider."