Pakistan is passing proposals between Iran and the US to keep talks alive behind the scenes and inch towards a peace agreement, officials and experts say.

Pakistani officials say that they are conscious of the fact that at stake is not only regional peace, but the health of the global economy and the livelihoods of millions of the poorest people in the world – including in Pakistan, whose monthly energy import bill has almost tripled as a result of the war.

Islamabad views the continuation of the ceasefire, in place for more than three weeks, as a major achievement. Tehran and Washington have said Pakistan remains the primary conduit for negotiation, and Pakistan’s prime minister, Shehbaz Sharif, said on Wednesday he had been promised a revised offer from Iran to pass on.

Pakistan’s role switched in recent days to a lower-profile but urgent task of running a backchannel, after momentum behind direct talks stalled. Islamabad believes the peace process can still make progress without a face-to-face meeting.

Both Iran and the US hardened their positions after the breakthrough of getting them into the same room in Islamabad for an all-night negotiation session in April, the highest-level engagement between the two sides since the 1979 revolution.

According to Tehran, those talks got close to a deal but the US abruptly walked out. Washington said Iran was not prepared to go far enough. An attempt to engineer a second round in Islamabad last weekend fell apart after the Iranian side refused to meet the US team, which was ready to fly in.

US officials briefed this week that Washington was considering returning to war. Some voices in Iran have expressed frustration that Pakistan has not been able to hold the US to commitments given in the negotiations.

Masood Khan, Pakistan’s former ambassador to the US, said Pakistan was not only transmitting messages between the two sides. He said Islamabad’s intervention had led to an initial two-week ceasefire, and the US-Iran meeting with Pakistani officials as referees. Islamabad persuaded Trump to extend the ceasefire, he said, which now has no stated deadline.

The next task was to convince both sides to simultaneously lift their blockades on the strait of Hormuz, he said. But Trump this week said the blockade was more effective than bombing, while Iran’s supreme leader, Mojtaba Khamenei, hailed a “new chapter” for the strait – suggesting neither side was about to back down.

“Pakistan is playing a complex role as a mediator,” said Khan. “Iran is signalling that it is playing a long game, but America wants quick results.”

Pakistan’s military chief spent three days in Tehran in April, meeting the country’s different power centres, while the prime minister worked on regional support for the peace process, visiting Saudi Arabia, Qatar and Turkey. Islamabad has enlisted countries as far afield as Japan to put their weight behind the diplomacy, and Pakistan’s foreign minister also spoke this week to Yvette Cooper, the UK foreign secretary.

“The clock on diplomacy has not stopped,” said Tahir Andrabi, the spokesperson for Pakistan’s foreign ministry, adding it would be helpful if the two sides spoke by phone in the absence of meetings. “The proposals old, new, not so new, not so old, are on the table.”

The last Iranian proposal, which offered to reopen the strait of Hormuz but defer resolving the issue of the country’s nuclear programme, was passed through Pakistan. Trump said Iran had to commit to not acquiring nuclear weapons.

Islamabad believes a deal remains within reach. But, it faces an Iran that is in danger of overplaying its hand, and a US administration that seeks total victory rather than a compromise.

Unresolved on the nuclear front is agreeing a pause on Iran’s uranium enrichment and an arrangement for its stockpile of highly enriched uranium.

Regional diplomats with knowledge of the discussions said it should be possible to agree on a moratorium on enrichment of about 10 years – roughly in the middle of the negotiating positions of the two sides. In place of the US demand to hand over the highly enriched uranium, it could be sent to Iran’s ally Russia, a possibility discussed this week between Trump and the Russian leader, Vladimir Putin.

Tehran has not agreed to let go of the highly enriched uranium, or the right to enrich.

Jauhar Saleem, formerly Pakistan’s top diplomat who is now president of the Institute of Regional Studies, a thinktank in Islamabad, said Iran’s apparent strategy of dragging out the negotiation, in the expectation of getting a better deal, was highly risky. But Washington also had to recognise that its pressure tactics had not worked on Iran over the years, he said.

“It is not realistic that Iran would give in to all demands,” said Saleem. “An agreement has to be a win-win situation for both sides.”