Democratic Congressman Jared Moskowitz has said the Trump administration is being too soft on Iran.
Mr Mokowitz's comments came shortly before the conclusion of a fourth round of talks in Oman between the US and Tehran regarding Iran's nuclear programme.
Iran's Foreign Ministry described the latest negotiations as "difficult but useful" and said the next round would be co-ordinated and announced by Oman in due course.
"Iran is the weakest they’ve been in a long time, now is not the time to appease them,” the Florida Democrat told Fox News Sunday.
"Now is the time to put maximum pressure on them and make sure that we dismantle the nuclear programme. I'm not saying we should start bombing the facility, but I'm saying all options should be on the table, right?”
Also on the show, Republican Senator Tom Cotton said he spoke to Steve Witkoff, the US envoy to the Middle East who led the US delegation in Oman, shortly before his departure for the talks.
“He's been very clear what President Trump's position is, and that position is that Iran cannot have the ability to enrich uranium," Mr Cotton said. "That's really the critical path to getting a nuclear weapon. So they can't have centrifuges. That's the unified position of the American government. That's been our position for many years.”
Mr Cotton also echoed the sentiment of Mr Mokowitz questioning internal stability and insisting on the potential vulnerabilities in Iran as a whole.
"The President believes it's possible to get a deal with Iran because of the pressure we've put on them, because of the economic pressure we've put on them and because, frankly, the ayatollahs are scared to death of Donald Trump, and they have been for eight years," he said.
The latest talks between the US and Iran figured large on both the cable and network versions of Fox programming on Sunday.
When asked about the discussions on Fox and Friends Weekend Edition, US Secretary of Energy Chris Wright, however, pivoted to the topic of Mr Trump’s much-anticipated visit to Saudi Arabia, Qatar and the UAE.
“The President’s agenda at home here is peace and prosperity in the US, and he has the same agenda for the Middle East, peace and prosperity for that region, which is achievable and within reach, but takes bold leadership and not the previous administration’s sole focus on the biggest troublemaker in the region,” Mr Wright said. “We’re going to visit our allies."
Mr Trump, who withdrew Washington from the 2015 deal between Tehran and world powers that was meant to curb Tehran's nuclear activities, has previously threatened to bomb Iran if no new deal is reached to resolve the long-running dispute.
Tehran has accelerated its enrichment programme since the previous deal collapsed but says it is purely for civilian purposes.
Although the US and Iran have reported progress in the latest talks, few details have been released.
A senior Trump administration official said that the latest discussions in Oman lasted more than three hours.
"Agreement was reached to move forward with the talks to continue working through technical elements," the official said.
"We are encouraged by today’s outcome and look forward to our next meeting, which will happen in the near future."
Mr Trump has suggested Iran would be a “great, happy country” if it signs an agreement, but he has also pursued a “maximum pressure” campaign built around tough sanctions aimed at shutting off Iranian oil exports.
Mr Cotton blamed former president Barack Obama for the Joint Comprehensive Plan of Action, as the nuclear deal was known, giving Iran too much leeway.
"Barack Obama's deal allowed them to have centrifuges and a vast nuclear infrastructure to enrich uranium,” he said.
"What you see here is the difference between, on the one hand, President Trump's America-first approach, which recognises the moral threat that a nuclear Iran poses to the United States, and what you might call the 'blame America first’ mindset, which says a bad deal is better than going to war ... that’s what Obama used to say.”
Mr Cotton said Mr Trump rejects that mindset.
