A Qatari natural gas tanker ​crossed the Strait of Hormuz on Sunday for the first time since the start of the Iran war, even as uncertainty persisted over peace efforts with Washington still awaiting Tehran's response to a proposal.

The QatarEnergy-operated carrier Al Kharaitiyat passed safely through the strait and was heading for Pakistan's Port Qasim, according to data from shipping analytics firm Kpler, said a Reuters report.

But Iranian authorities said vessels from countries that follow US sanctions against Iran would face problems crossing the Strait, ​the semi-official Tasnim news agency said.

Earlier, Bloomberg reported that Saudi Aramco and Abu Dhabi National Oil Company moved limited crude cargoes through the Strait of Hormuz despite ongoing threats and shipping disruptions tied to the Iran conflict.

According to tanker-tracking data compiled by Bloomberg, non-Iranian crude exports through Hormuz have averaged roughly 500,000 bpd since the beginning of March, compared to about 13.6 MMbpd during the two months before the conflict escalated.

Despite the shipping breakthrough, there was no visible movement on the diplomatic front.

US Secretary of State Marco Rubio said on Friday that Washington expected Iran to respond within hours to a US proposal that would formally end the war before opening negotiations on broader issues, including Tehran's nuclear programme. But by Saturday evening, Iran had yet to publicly deliver its response, which had been expected earlier in the day.

Rubio met Qatari Prime Minister and Foreign Minister Mohammed bin Abdulrahman Al Thani in Miami on Saturday, where they discussed the need to continue working together "to deter threats and promote stability and security across the Middle East," according to US State Department spokesperson Tommy Pigott.

*This report has been updated.