The United States has not confirmed whether Chen is in its diplomatic quarters in Beijing, but supporters have said he is under US protection.
"We call on the Chinese authorities to exercise utmost restraint in dealing with the matter, including avoiding harassment of his family members or any person associated with him," the Delegation of the European Union to China said in a statement.
"Human rights defenders should be treated in full compliance with Chinese laws and constitution."
Chen escaped after 19 months of house arrest on April 21, since when several supporters have been detained by police. Most have since been released.
British Foreign Secretary William Hague voiced concern about Chen's case, which he said had exposed "abuse of power", and urged Beijing to guarantee the safety of Chen's family.
"We will now monitor the status of Chen's family and associates and we look to the Chinese government to guarantee their rights, freedoms and personal safety," he said at a news conference in London to release the British foreign ministry's annual human rights report, which mentions Chen's case.
"We remain concerned about the health of Chen's wife and daughter and we will continue to work with other European Union countries to raise our concerns on this with the Chinese government," Hague said.
He said he could provide no information about Chen's whereabouts "but we remain very concerned about this case and I think there is an opportunity here for the Chinese authorities to show they will not tolerate the abuse of power which Chen's case has exposed in many ways".
Chen, a self-schooled legal advocate who campaigned against forced abortions under China's "one child" policy, was held under extra-legal detention in his village home in Linyi from September 2010, when he was released from jail for charges he said were spurious.
Chen's wife, Yuan Weijing, and child did not escape with him, and human rights activists have voiced worry that they and Chen's other relatives might have suffered abuse at the hands of police and officials angry about his escape.
Contention over Chen's future threatens to overshadow a visit by U.S. Secretary of State Hillary Clinton and Treasury Secretary Timothy Geithner, who are due in Beijing this week for the annual "strategic and economic dialogue" between the two countries. (Editing by Nick Macfie)