If European countries continue to support Iran's uranium enrichment, the United States should "grind them into the ground" with sanctions, Sen. Lindsey Graham said.

Graham's warning comes days after Tehran announced it was beginning to enrich uranium beyond limits set forth in the 2015 Iran nuclear agreement. European signatories to the deal have attempted to salvage the agreement after President Trump withdrew the United States last year.

"They are just weak," the South Carolina Republican told Fox News Channel host Maria Bartiromo on Sunday Morning Futures. "They don't care if the ayatollah enriches himself as long as they can do business."

Graham said a better deal would prevent Iran from enriching any uranium. The nuclear deal allows Iran to maintain a limited stockpile of low-enriched uranium, though the regime surpassed that limit last month and has started enriching at a higher level than allowed. Uranium enriched to 90% or higher is required to make a nuclear weapon. Iran is limited to 3.67% enrichment under the deal, though experts note increasing the enrichment rate is a fairly simple process. The United Nations has verified Iran is now enriching to just under 5%.

To get European countries on board with the Trump administration's strategy, Graham said he would force them to decide with whom they would rather do business.

"I will tell the Europeans, 'If you want to side with the Iranians, be my guest, but you won't use an American bank or do business with the American economy,'" Graham said.

"You need to pick the ayatollah or the United States. Those are your choices."

"Are you prepared to sanction whatever company or country within Europe does?" Bartiromo asked.

"To the ground," Graham replied.

Iran has pressured European signatories to come up with a solution to the U.S. sanctions regime. Europe created the Instrument in Support of Trade Exchanges, a bartering system that is meant to allow trade with Iran by bypassing the U.S. financial system, but it has not been used to conduct sanctioned trade, and Iran says Europe needs to do more as the U.S. "maximum pressure" strategy squeezes its fragile economy.

The Trump administration's most recent round of sanctions directly targeted Ayatalloh Ali Khamenei's massive business empire. The Treasury Department was expected to announce sanctions against Iranian foreign minister Javad Zarif, but has not done so. In fact, the State Department just granted Zarif a limited visa ahead of his visit this week to the United Nations in New York City.

Tensions between the United States and Iran have risen drastically in the last several months, leading to an increased U.S. military presence in the Middle East. The Strait of Hormuz, a narrow waterway key to the Middle Eastern oil trade, has been a focal point of the dispute after Iran threatened to attack British shipping earlier this month and mined a Japanese tanker in mid-June. Iran shot down a U.S. drone near the Strait of Hormuz on June 20, which nearly led to a retaliatory strike Trump called off at the last moment.

While the United States has yet to retaliate against Iran with military force, Graham said he sees two "red lines" that would require such a response.

"If they go to enrichment to the levels they are talking about, if they try to restart the heavy water reaction in [Iran], I would consider that a red line," Graham said. "I would not let them cross."