At the same time, Price did not name specific vessels or companies that could be affected by the US restrictions.
He reaffirmed the US stance, describing the pipeline as a "Russian geopolitical project" and a "bad deal" for Europe.
"We are closely monitoring sanctionable activity. As we collect that information, as we analyze the facts, we are applying those facts to the requirements laid out in this legislation," the spokesperson said.
US Department of the Treasury has imposed sanctions on the Cyprus-based company Transadria and the Russian-flagged vessel Marlin on Tuesday.
Also on Tuesday, the Kremlin fired back at possible new sanctions from Washington against Nord Stream 2, branding them illegal and wrong, especially in light of the attempts at re-establishing the previously lost dialogue between both countries.