"If we win the election, Iran will come and sign an agreement with us very rapidly. I would say within a week, but let's give ourselves a month," he claimed during a September 10 news conference at the White House.
Trump notably withdrew the US from the 2015 Joint Comprehensive Plan of Action (JCPOA) agreement, or Iran nuclear deal, on May 8, 2018, citing Tehran's continued "pursuit of nuclear weapons and the means of delivering them."
US Secretary of State Mike Pompeo recently made the same argument to the United Nations Security Council after the US set forth a resolution to extend the international arms embargo against Tehran - set to expire October 18.
"We will never allow the Islamic Republic of Iran to have a nuclear weapon," the Washington official vowed.
However, US allies France, Germany and the United Kingdom openly declared that Washington's push to invoke the "snapback" mechanism was actually in violation of the JCPOA, which is still being upheld by its remaining signatories.
"We remain committed to the JCPOA despite the significant challenges caused by US withdrawal," the countries wrote. "We believe that we should address the current issue of systematic Iranian non-compliance with its JCPOA obligations through dialogue between JCPOA participants."
Trump's statements on Tehran's willingness to enter a new agreement come days after Iranian President Hassan Rouhani asserted "the path is clear" for the US to reenter the JCPOA "any day," so long as Washington "decides to admit to its mistakes, make up for its illegal actions and return to Resolution 2231."
Iranian nuclear chief Ali Akbar Salehi announced on Tuesday that Tehran has initiated construction near its Natanz nuclear site on a "modern, larger and more comprehensive" production hall for advanced uranium enrichment centrifuges.
Troop Drawdown to Leave 'About 2,000' US Soldiers in Iraq - Trump
The US president also announced that the Trump administration intends to reduce the number of American troops deployed to Iraq.
"Iraq, we'll be down to about 2,000 soldiers in a very short period of time," he said.
Some 5,200 US troops are presently deployed to Iraq.
Trump's Thursday comments come contrary to those issued a day prior by US Central Command chief Gen. Frank McKenzie.
McKenzie, the top US general in the Middle East, detailed that the country will cut its troop presence in Iraq to 3,000, translating to the departure of some 2,200 US soldiers from the country.
Additionally, some 4,100 US troops would be leaving Afghanistan - which currently hosts 8,600 American soldiers - McKenzie told reporters on September 9. Trump echoed this estimate on Thursday, noting that a smaller number of troops would remain in Syria to patrol the embattled country's northeast oil fields and provide military assistance to Kurdish forces in the region.