The state-controlled papers across the country attacked the weekend comments by Mr Chen that China and Taiwan were both separate countries.
Taiwan officials continued to try to play down the incident, quoting Mr Chen as saying his comments had been misread.
"My comments were oversimplified and may have caused misunderstanding," Chang Chun-hsiung, secretary-general of President Chen's Democratic Progressive Party (DPP), quoted Mr Chen as saying at the conclusion of a meeting of party leaders.
The US tried not to get involved in the dispute, saying only that its policy towards China and Taiwan was "well known and unchanged".
Chinese newspapers were full of quotations from analysts and members of the public that Mr Chen should not have diverged from the line that Taiwan will eventually rejoin the mainland it split from more than 50 years ago.
But the papers stressed there was no argument with the majority of Taiwanese people, merely the small number of politicians intent on "splittist activities".
In Taiwan, opinion polls provided a mixed picture. One poll suggested support for Mr Chen's backing of a referendum, another suggested the incident had dented his popularity.
'Untrustworthy, naive'
The online edition of the official People's Daily was scathing in its criticism of Mr Chen in an article headlined: "Words show untrustworthiness and political naivety".
The article said: "Sometimes, it's hard to assess a man's wisdom or sanity until he speaks up.
"Having said that each side across the [Taiwan] Strait is a country, Chen might feel quite relieved, unaware, however, that he has actually confessed his lack of two valuables to a leader: trustworthiness and good judgement."
The paper, which is the official daily of the ruling Communist Party, quoted the vice-chairman of the national committee of China's top advisory body, the Chinese People's Political Consultative Conference, as saying Mr Chen's remarks were irresponsible.
Ma Man-kei of Macau said: "Chen is betting on the happiness of more than 20 million Taiwan compatriots and seeking to drive them onto a road of anguish."
He called Mr Chen's comments representative of "splittist activities by a small force" and urged the Taiwanese leader to "rein in at the brink of the precipice".
Taiwan's top official for China policy, Tsai Ing-wen, is expected to use a brief stopover in the US to reassure the Bush administration that Taiwan's China policy has not changed.
Ms Tsai, travelling on an overseas tour with Premier Yu Shyi-kun, has called on people not to "over interpret" President Chen's comments.