"We swim together or we sink together," he said, calling for tighter Asia-Europe co-operation in order to survive the crisis.
"I very much hope that China can make an important contribution to the solution to the financial crisis. It's a great opportunity for China to show a sense of responsibility."
European governments have already committed more than $2 trillion to banks and money markets in efforts to shore up investor confidence.
But unlike Europe's co-ordinated effort, Asian governments have for the most part limited their intervention to cutting interest rates, guaranteeing bank deposits and injecting money into the credit markets.
Barroso said the two regions "face challenges which don't respect any borders".
'No one immune'
"No one in Europe or Asia can seriously pretend to be immune. We are living in unprecedented times, and we need unprecedented levels of global co-ordination."
On Thursday Hu Jintao, the Chinese president, said the world economy looked "grim and complicated".
"The emerging markets and developing countries are confronted with financial risks, weak foreign demand and mounting inflation," he was quoted as saying by China's Xinhua news agency.
Nicolas Sarkozy, the French president, has said he will seek Asian backing for his bid to radically restructure the Western-dominated global financial system.
Sarkozy, who currently holds the rotating European Union (EU) presidency, wants the emerging giant economies of China and India to have a bigger role in the world's economic decision-making.
Liu Jianchao, a Chinese foreign ministry spokesman, agreed that there was a need to "explore the possibilities for reform of the international financial structure" but gave no specifics on how to stabilise the markets.
Meanwhile, a diplomatic spat threatened to derail the summit's main agenda after the European Parliament on Thursday awarded its top human rights Sakharov Prize to Hu Jia, an activist imprisoned by the Chinese government on subversion charges.
In criticising the move, Liu raised China's "strong dissatisfaction at the decision by the European Parliament to give the award to a jailed criminal in China, in disregard of our repeated representations".
The spokesman, however, later tried to downplay any impact the move may have on the two-day biennial summit.