However, one of the sources, a senior security official, said Iran's overnight strikes on Saudi Arabia's industrial facilities linked to US firms threatened to derail the talks.
If Saudi Arabia were to retaliate, the talks would be over, the source said, adding that could draw Pakistan into the conflict under its defence pact with Saudi Arabia which binds both countries to fight for each other in case of a war.
A second source with knowledge of the talks said Iran was "walking on thin ice" and that the next three to four hours were critical for the future of dialogue.
Pakistan has been the main go-between for proposals shared by both sides but there has been no sign of a compromise.
"We are in touch with the Iranians. They have lately shown flexibility that they could join the talks but they are at the same time taking hard lines as a prerequisite for any negotiations," the Pakistani security source said.
He added that Pakistan was persuading Iran to enter negotiations without prior conditions.
Trump threatened that "a whole civilisation will die tonight" if Iran did not open the Strait of Hormuz.
Trump has given Iran until 8pm in Washington DC on Tuesday (10am on Wednesday AEST) - 3.30am in Tehran - to end its blockade of Gulf oil or the US will destroy every bridge and power plant in Iran.
Iran says it would retaliate against US allies in the Gulf, whose desert cities would be uninhabitable without power or water.
As the clock ticked down on Trump's deadline, strikes on Iran intensified, hitting railway and road bridges, an airport and a petrochemical plant.
US forces attacked targets on Kharg Island, home to Iran's main oil export terminal.
Iran's foreign ministry spokesman said on Monday that messages are still being exchanged between Iran and the US via mediators.
A senior Iranian source said Iran had rejected a proposal for a temporary ceasefire with talks dependent on an end to US-Israeli strikes and compensation for damages.
Pakistan's foreign office said on Tuesday that the strikes on Saudi Arabia constitute a dangerous escalation.
"Such unwarranted aggressions have serious repercussions, to spoil the ongoing peaceful options and conducive environment," added a Pakistani army statement after top commanders met with army chief Asim Munir.
Pakistan wants to avoid being pulled into the war, which could wreak havoc along its shared western border with Iran and roil discontent among its large Shi'ite population, the second largest in the world after Iran.
Analysts say the defence agreement may not trigger immediate military action but could be activated if conflict escalates.
Iran's willingness to risk embarrassing Pakistan at a time when "it is crucial to brokering a ceasefire reveals just how committed Tehran is to a tit-for-tat strategy that punishes the Gulf for US and Israeli strikes," said Adam Weinstein, an expert on Pakistan, Afghanistan and US politics at the Quincy Institute.
