"We reaffirm that a credible military threat remains on the table and we underscore the imperative that the current sanctions be maintained aggressively, and call on you to increase pressure through sanctions already in place," according to the letter.
The letter comes as Western diplomats from the P5+1 group — the five permanent United Nations Security Council members and Germany — are gearing up for the next round of talks with Tehran on its nuclear enrichment program.
Iran has long maintained its nuclear ambitions are strictly peaceful and an attempt to solve the country's energy needs.
However, the United States and its allies argue Tehran's enrichment program is squarely aimed at developing a nuclear weapon.
But the most recent round of talks comes amid efforts by Iranian President Hassan Rouhani to re-establish ties with Washington, a move that has surprised many U.S. diplomats and long time Middle East observers.
That said, McCain and other Senate Republicans remain wary of Iran's "charm offensive" with the United States.
"We must see transparent, tangible, and verifiable steps by the Iranian regime to fulfill its international obligations" on all fronts before the White House can begin rebuilding its ties with Iran, McCain, Graham and Ayotte said in a statement in September.
In Monday's letter, lawmakers expressed optimism over Rouhani's recent diplomatic overtures to Washington and its allies.
But that optimism was tempered by concern that Tehran would not follow through with promises to the White House on its nuclear program.
"If Iranian actions fail to match the rhetorical reassurances of the last two weeks, we are prepared to move forward with new sanctions to increase pressure on the government in Tehran," they wrote.
In August, the Treasury Department's Terrorism and Financial Intelligence directorate levied a series of economic sanctions against top commanders from Hezbollah's "Unit 1800."
The unit is tasked with providing weapons, equipment and training to radical militant groups affiliated with the Lebanese terrorist organization around the world, with the explicit backing of the Iranian government, according to a department statement issued Thursday.
Most recently, Unit 1800 members have been actively supporting militants looking to destabilize the democratic government in Iraq and bolster the Assad regime.
That said, Iran remains “the most active state sponsor of terrorism” with Tehran continually carrying out "deplorable abuse of basic human rights, denial of basic civil freedoms ... [and] ongoing activities that seek to destabilize the region," according to the letter.