As the Iran war enters its fourth week, the US president said the United States and Iran have had "very good and productive conversations" that could yield "a complete and total resolution" to the war, according to reports.

Posting on his social media on Monday, the US leader said he has extended his deadline for Iran to reopen the Strait of Hormuz, adding that the US will hold off on its threatened power plant strikes for five days while the talks continue.

Iranian media on Monday denied the reports, quoting Iranian officials and sources.

However, the US leader's post has signaled that dialogue may be possible.

Although the conditions of the two sides for a ceasefire have been far apart, with both sides presenting terms as victors, they each have reasons to bring an end to the conflict.

The US' expectations were a quick war and regime change, neither of which has materialized. Questions such as what are the objectives and the plans for achieving them and how and under what conditions should the war be concluded remain to be answered. Meanwhile, the divergences between the US and Israel over priorities, risk tolerance and long-term objectives have become ever more apparent.

Meanwhile the US allies in Europe and the Gulf have been pushing for de-escalation, putting further pressure on the US. At the same time, domestic politics, market disruptions and rising anti-war sentiment in the US are all potential brakes on what the US administration can do.

Although Iran harbors a strong desire for revenge and seeks to completely eliminate the bases for the US to wage another war against it, the war is primarily taking place on its own soil, costing Iranian lives and causing significant destruction to its infrastructure.

While there is little hope of either side accepting the other's demands as previously stated and there appeared to be no meeting point within their respective stated conditions, the latest reports suggest that efforts may be being made to open dialogue. This would certainly be in both sides' interest.

But for the "very good and productive conversations" that could yield "a complete and total resolution" to the war as the US president said, the US will have to keep a tight rein on Israel.

Tel Aviv will no doubt be aware if any talks are taking place. It remains the wild card as its objectives differ from those of the US. With the regional spillover effects of the conflict threatening to draw the US deeper into another costly entanglement, including the potential catastrophic mess of a ground offensive, the US risks further losses if it lets Israel continue to lead it further into the abyss.

Israel has intensified its military campaign against Lebanon. On Sunday, Israeli warplanes struck the Qasmiyeh Bridge over the Litani River in southern Lebanon, a critical infrastructure link, with Lebanese President Joseph Aoun condemning the strikes as a "prelude to a ground invasion". This escalation threatens to widen the conflict into a prolonged regional war, further destabilizing an already volatile region.

The world will be holding its breath in the hope that there are talks that do produce a ceasefire that opens the Strait of Hormuz. The US threat to strike Iran's energy facilities if Tehran didn't open the strait had further raised global concerns about energy supplies and the effect on the world economy.

As such, a ceasefire and peace talks between the US and Iran would be welcome. The US as the one that started the conflict should pursue talks by making rational and pragmatic moves to show it is willing to negotiate in good faith.

If a nascent diplomatic channel has been opened, Washington must moderate its previously uncompromising stance and pursue a ceasefire before the window for peace slams shut.