However, the measure has divided the 15-member Security Council, with Russia, China and France – who each hold veto privileges – all voicing strong objections.
Italy’s Foreign Minister Antonio Tajanialso, who joined the virtual talks, called for a “humanitarian corridor” for fertiliser and other essentials through the strait to avoid a food disaster in Africa.
Cooper earlier slammed Iran’s “recklessness” over the strait as she kicked off the virtual meeting.
She said Iran’s blockade of the waterway was “hitting our global economic security”.
Around a fifth of the world’s oil and liquefied natural gas passes through the strait in peacetime.
A total of 37 countries have signed a statement, first published last month, expressing “readiness to contribute to appropriate efforts to ensure safe passage through” the shipping lane.
Britain, France, Germany, Italy, Japan and the Netherlands are among those to have signed it.
The United States, China, and most Middle Eastern countries have not, according to a list provided by the UK government.