Deloitte's Touche Tohmatsu said it was "unfortunate" the two countries could not find common ground but added: "We remain hopeful that a diplomatic agreement can be reached."
The Chinese branches of Ernst & Young and KPMG also said they still supported work between US and Chinese regulators toward sharing of information and mutual understanding.
BDO did not immediately respond to a request for comment.
Last year, the SEC took Deloitte to court to try to force it to turn over documents in connection with an investigation into China's Longtop Financial Technologies Ltd. In July, it sought a six-month delay in that legal battle, citing negotiations with Chinese regulators.
On Monday, the SEC said those talks had failed.
"Only with access to work papers of foreign public accounting firms can the SEC test the quality of the underlying audits and protect investors from the dangers of accounting fraud," said Robert Khuzami, director of its enforcement division.
"Firms that conduct audits knowing they cannot comply with laws requiring access to these work papers face serious sanctions."
The SEC said its enforcement arm has been cracking down on China-based audit firms as part of an initiative to "address concerns arising from reverse mergers and foreign issuers."