The conditional offer comes amid intense diplomatic engagements by Islamabad for a possible second round of high-stakes talks between the two sides to end the weeks-long Middle East conflict.
"Washington's priority is still the suspension of Iran's uranium enrichment program for at least 20 years in exchange for sanctions relief and the freezing of the Islamic Republic's financial assets," a senior Pakistani government source, who is familiar with the back-channel diplomacy, told Anadolu on request of anonymity.
"But Washington has shown its conditional willingness to reduce the moratorium timeframe from 20 years to 10 years if Tehran gives some strong guarantees about its (US) nuclear weapons concerns," the source said, without elaborating what kind of guarantees the US demands.
On Saturday, Iran’s Supreme National Security Council, in a statement, said Tehran was reviewing “new proposals” received from the US, even as it warned that its negotiators would cut no compromises with Washington.
The statement came after Pakistan's army chief, Asim Munir, met with Iran's civil and military leadership last week during a three-day trip that concluded on Friday.
Munir is directly involved in mediation between the US and Iran to end the war. He has spoken to US President Donald Trump several times.
According to sources, Pakistan is working to close the "gap" on the thorny nuclear issue, which remains a major impediment to a negotiated settlement.
Background interviews with Pakistani sources and diplomats suggest that Washington and Tehran are still exchanging "messages and proposals" through Islamabad in an effort to reach a "maximum understanding" before the two warring sides reconvene at the table.
Other US proposals include transferring Iran's enriched uranium for 10 years, "preferably to the US or a third country," the sources added.
Iran has publicly rejected the idea, saying it will not hand over its enriched uranium to a third country.
Russia proposed taking possession of Iran's highly enriched uranium as a diplomatic solution to the ongoing conflict, but Washington turned down the offer, Kremlin spokesman Dmitry Peskov told India Today TV last week.
Iran is said to have over 400 kilograms (882 pounds) of enriched uranium, and Tehran has proposed that it can suspend nuclear activity for up to five years, according to The New York Times.
Iran has consented to Islamabad's proposal for a third-party monitoring of Tehran's nuclear program by four countries in collaboration with the UN nuclear watchdog International Atomic Energy Agency (IAEA), the sources said.
Iran has conveyed its agreement to Munir, while Washington has not shown "any interest" in the proposal, they noted.
Another source privy to the matter told Anadolu that despite their "apparent inflexibility," the two sides are expected to reach a "middle ground" to break the stalemate.
"Both sides acknowledge the fact that war will further complicate this already complex issue. That's why we are very hopeful that they (Washington and Tehran) will agree on some middle ground," the source added.
The US has long demanded “strict and comprehensive” monitoring to ensure that Iran does not build a nuclear weapon.
The intense diplomatic efforts by Islamabad come to smooth the way for the second round of talks between the US and Iran, expected any time soon in the Pakistani capital.
Tehran, however, said it would not participate in the much-awaited talks until the US ends its "illegal" blockade of Iranian ports.
Washington demands the reopening of the Strait of Hormuz, which has been lying nearly closed since the US and Israel initiated their attacks on Iran on Feb. 28.
Tehran declared the strait open on Friday but closed it a day later after Trump announced that the blockade of Iranian ports would continue, and on Sunday, the American forces detained one Iranian cargo ship after they opened fire and boarded it.
Pakistan took center stage when it brokered a two-week ceasefire between the US and Iran on April 8, followed by critical talks in Islamabad attended by senior delegations from both countries on April 11 and 12. However, neither side was able to reach an agreement to bring the Middle East war to an end.