Relations between the two sides have deteriorated sharply since Trump took office last month promising a tough line on what he sees as Iranian belligerence toward US interests.
"Iran would do well to look at the calendar and realize there's a new president in the Oval Office. And Iran would do well not to test the resolve of this new president," Pence told ABC News in an interview taped Saturday.
The charged rhetoric has raised questions over whether the United States will abandon commitments it made under a landmark deal - negotiated with several world powers and approved by president Barack Obama in 2015 - that obliged Iran to curtail its nuclear program in exchange for relief from US and international sanctions.
"The Iranians got a deal from the international community that again, the president and I and our administration think was a terrible deal," Pence said.
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"Well, we're evaluating that as we speak," he said.
"I think the president will make that decision in the days ahead. And he'll listen to all of his advisors, but make no mistake about it. The resolve of this president is such that Iran would do well to think twice about their continued hostile and belligerent actions."
US officials said the new sanctions imposed Friday were in response to Iran's recent ballistic missile test and its support for the Huthi rebels in Yemen, who recently targeted a Saudi warship.