Jose Manuel Barroso's comments came as the leaders of 45 countries
prepared to meet in Beijing at the weekend for the seventh Asia-Europe
Meeting (ASEM).
Mr Barroso also said the situation was "a great opportunity for China to show a sense of responsibility".
Human rights are also expected to feature heavily in talks.
This follows several recent diplomatic incidents over the issue.
"The present gathering could not be more timely," Mr Barroso
told reporters in Beijing. "We face challenges which don't respect any
borders.
"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."
Mr Barroso said the world needed Asia - particularly China, India and Japan - to "be on board.
"It's very simple: we sink together or we swim together.
"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."
He also said the commission believed China should be given a greater voice in international financial institutions.
Chinese foreign ministry spokesman Liu Jianchao said China would
co-operate more closely with other countries on economics, but gave no
specific details.
"We need to explore the possibilities for reform of the
international financial structure so that we can make joint efforts to
stabilise markets," he said.
Sensitive talks
The economy is expected to dominate that summit but Mr Barroso said it
was important that it discussed "all matters, including sometimes the
most sensitive ones".
Analysts have said the summit is likely to be overshadowed by the
awarding of a major European Parliament human rights prize to a
prominent Chinese dissident on Thursday.
Hu Jia is currently serving a three-and-a-half year jail sentence for political subversion.
China had urged the parliament not to give the Sakharov Prize to
Mr Hu and said doing so was "a gross interference in China's domestic
affairs".
But foreign ministry spokesman Mr Liu said he did not think it would affect the talks.
Patching up ties
The summit is German Chancellor Angela Merkel's first visit to
China since she met the Dalai Lama when he visited Berlin a year ago.
China reacted angrily to the meeting, as it regards the Dalai
Lama as a separatist leader, and the incident led to a cooling of
relations between the countries for several months.
Mrs Merkel was greeted by Chinese President Hu Jintao and
Premier Wen Jiabao in a welcoming ceremony at the Great Hall of the
People.
She toured a factory which produces Mercedes-Benz cars, telling
workers they were "a very good example of German-Sino economic
co-operation".
Mr Hu has also held meetings with Italian Prime Minister Silvio
Berlusconi, Dutch Prime Minister Jan Peter Balkenende and Donald Tusk,
Polish prime minister, among others.
As well as economics, climate change, trade, energy and food
security are expected to be on the summit agenda but analysts say it is
largely a talking shop and it not expected to make any major decisions.