In what is being broadly read as a sign of easing tensions with Iran, and a perceived gesture of goodwill, the Pentagon confirmed the USS Nimitz carrier strike group had left the Middle East for the Indo-Pacific.

At the same time, both Washington and Teheran are moving forward from their respective earlier shows of willingness to re-engage under the 2015 Iran nuclear deal.

All stakeholders, the European Union in particular, should take advantage of these precious latest developments to encourage and facilitate the return of the US to the hard-earned agreement as soon as possible, and Iran's full compliance with it.

The previous US administration of Donald Trump withdrew from the 2015 nuclear deal, officially the Joint Comprehensive Plan of Action, and imposed new sanctions on Teheran in the hope of debilitating it with "maximum pressure". The ill-conceived move backfired, escalating US-Iran tensions and prompting the latter to threaten to forsake its obligations under the agreement.

Washington's and Teheran's latest exchange of olive branches is a laudable first step on the part of both parties, the momentum of which must be carefully preserved.

But both parties want the other to act first, so it can reciprocate.

"If Iran comes back into full compliance with its obligations under the JCPOA, the United States would do the same," said US State Department spokesman Ned Price.

Iranian Foreign Minister Mohammad Javad Zarif, however, wanted to see Washington display sincerity. "The United States needs to come back into compliance and Iran will be ready immediately to respond," Zarif said. "The timing is not the issue. "

Should both sides insist on the other making the first move, all shows of willingness may prove to be meaningless. And simultaneousness, on an issue of such complexity, would be difficult to execute.

Although Zarif told CNN International interviewer Christiane Amanpour, "You know clearly there can be a mechanism to basically either synchronize it, or coordinate what can be done."

This is an unmistakable message of flexibility from Teheran that allows the possibility of navigating an exit in an otherwise unavoidable diplomatic stalemate.

He entrusted to EU foreign policy chief Josep Borrell the role of choreographer because of his position as coordinator of the 2015 deal. Borrell is clearly amenable as he has been, "working extremely hard to get the JCPOA back on the rails".

Since Zarif expects Borrell to "sort of choreograph" the actions Washington and Teheran need to take, there should be a possibility of success.

Both Zarif and US State Secretary Antony Blinken have expressed realism about the timetable, acknowledging it will take time for some specific tasks. Maintaining the constructive momentum by making headway in a pragmatic manner is now crucial.