Iranian Foreign Ministry spokesperson Esmaeil Baghaei later confirmed that Tehran's views had been "conveyed to the American side through Pakistan" but gave no details.
A fragile ceasefire is in place after six weeks of war that followed US-Israeli airstrikes on Iran, but talks mediated by Pakistan have stalled and US President Donald Trump has said the ceasefire is "on life support".
The Pakistani source gave no details of the revised proposal. Asked if it would take time to close gaps, the source said the sides "keep changing their goalposts" and added: "We don't have much time."
Washington has urged Tehran to dismantle its nuclear program and lift an effective blockade on the Strait of Hormuz, which normally carries one-fifth of the world's oil and liquefied natural gas supply.
Iran has demanded compensation for war damage, an end to a US blockade of Iranian ports and a halt to fighting on all fronts, including in Lebanon, where Israel is battling the Iran-backed Hezbollah militia.
Trump said in a post on Truth Social at the weekend that "the Clock is Ticking" for Iran, adding that "they better get moving, FAST, or there won't be anything left of them. TIME IS OF THE ESSENCE!"
Trump is expected to meet top national security advisers on Tuesday to discuss options for resuming military action, Axios reported.
Issues holding up negotiations also include Iran's nuclear ambitions. The US and other major powers want to ensure that Iran cannot develop nuclear weapons.
Tehran denies trying to do so, and also wants compensation for war damage, a guarantee that there will be no further attacks, and resumption of Iranian oil sales.
Baghaei said Tehran was prepared for all scenarios.
"As for their threats, rest assured that we are fully aware of how to respond appropriately to even the smallest mistake from the opposing side," he told a televised weekly press conference.
Hostilities have been scaled down since the ceasefire came into effect in April, but drones have been launched from Iran towards Gulf countries hosting US military bases.
One drone strike caused a fire at a nuclear power plant in the United Arab Emirates, officials there said on Sunday, and Saudi Arabia reported intercepting three drones.
Iran stepped up attacks on the UAE this month after Trump announced a naval mission to try to open the Strait of Hormuz, which he suspended after 48 hours.
Global share markets slipped on Monday as the latest drone attacks pushed oil prices and bond yields higher, stoking inflation worries.
Trump, who faces midterm elections in November that carry political risks for his Republican Party, held talks with Chinese President Xi Jinping last week without securing an indication from China that it would help resolve the conflict.
The disruption to shipping through the Strait of Hormuz has caused the biggest oil supply crisis in history, increasing crude prices by 50 per cent or more.
Some White House officials worry that Trump's foreign policy gamble and its effect on US gasoline prices may derail Republican chances of keeping control of Congress at a time when war-wary voters are more concerned with the cost of living than conflicts abroad.
