But granting equivalence depends very much on the specific conditions of individual sectors and countries when the decision was made, he said.
"If these conditions change, we will have to reassess the situation," Dombrovskis said.
The European Commission can unilaterally scrap an equivalence decision by giving a month's notice.
Dombrovskis' warning could equally apply to Britain, whose financial firms may need to rely on "equivalence" rulings after the country leaves the bloc in 2019. Some pro-Brexit campaigners say departure would allow Britain to ditch some EU rules.
London will only continue to thrive as an international financial centre on the basis of a strong, international regulatory system, he said.
Trump's regulatory review has also raised questions about future international rulemaking at bodies like the Basel Committee on banking standards, and the Financial Stability Board (FSB), which coordinates regulation across the Group of 20 economies (G20).
G20 finance ministers and central bankers meet in Germany in March and their communique will be scrutinised for signs of discord between the United States and other members over regulation.
Dombrovskis said there were strong arguments for continued international cooperation at Basel and the FSB, but for this to happen there was a need for "partners to cooperate with".
He singled out a letter from a U.S. lawmaker telling U.S. Federal Reserve Chair Janet Yellen not to negotiate new international banking rules.
Dombrovskis said there was a need to preserve European values like free rational thought, tolerance, solidarity and openness when threatened by "alternative facts" in financial and other sectors.
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