The issue was discussed in a meeting with the visiting Indian Foreign Secretary Vijay Gokhale, Pompeo told reporters at a news conference here, without providing insight into it.
"We are asking the same thing of India as we are of every country: Do not be the economic lifeline for the Maduro regime. So we talked about (Venezuela) I certainly won't characterize the conversations; they're private conversations," Pompeo said in response to a question.
"In the same way that India has been incredibly supportive of our efforts in Iran, I'm confident that they too understand the real threat to the Venezuelan people. We had a good conversation around that," Pompeo said.
At a news conference, Pompeo said the nations that support Venezuelan President Nicolas Maduro are, by the nature of this "illegitimate" regime, carrying out the very foreign interventionism of which they accuse others.
"Today, the United States is drawing a clear line between those who aid the forces of repression and those who give life to the Venezuelan people's democratic dreams. There is no ambiguity here about the truth," he said.
Similar kind of warning to other nations was issued by US National Security Adviser John Bolton.
"The United States will not stand idly by while foreign financial institutions facilitate illegitimate transactions that benefit Maduro and his cronies, and perpetuate the corruption that has devastated Venezuela," he said.
Earlier in the day, the Treasury sanctioned a Russia-based bank attempting to circumvent US sanctions on Venezuela's state-owned oil company PDVSA. It sanctioned Evrofinance Mosnarbank, a Moscow-based bank jointly owned by Russia and Venezuela, for being involved in facilitating illegitimate transactions that prolong Maduro's usurpation of democracy, it said.
"The illegitimate Maduro regime has profited off of the suffering of the Venezuelan people," said US Treasury Secretary Steven Mnuchin.
"This action demonstrates that the United States will take action against foreign financial institutions that sustain the illegitimate Maduro regime and contribute to the economic collapse and humanitarian crisis plaguing the people of Venezuela," he said.
In another tweet, Bolton asked international banks not to have relationship with the maduro regime.
"Bankers: Do not help Maduro and his accomplices steal the assets of the Venezuelan people. The United States is watching. The world is watching. The Venezuelan people are watching," he said.
Maduro is facing a challenge from opposition leader Juan Guaido who declared himself acting president in January.
The US views Guaido as Venezuela's legitimate leader and has imposed sanctions on the country's oil sector besides taking other actions targeting top government officials.