"This attack disrupted and posed a risk to the safety and security of international shipping and was a clear violation of international law," the countries said in a letter to the 15-member council seen by Reuters. "This act must be condemned by the international community."
Tehran has denied any involvement in Thursday's attack on the Mercer Street - a Liberian-flagged, Japanese-owned petroleum product tanker managed by Israeli-owned Zodiac Maritime. Two crew members, a Briton and a Romanian, were killed.
Diplomats said Britain was expected to raise the issue in a closed-door meeting of the Security Council in the coming days. The council is also coincidentally due to discuss maritime security in a public meeting on Monday, chaired by Indian Prime Minister Narendra Modi. India is council president for August.
"The United Kingdom and Romania, along with regional and international partners, are conducting a thorough investigation of this attack. We will update the council in due course," Britain, Liberia and Romania said in the letter.
Israel wrote separately to the UN Security Council, vowing to "continue to take all necessary measures to protect its citizens."
"Iran's unceasing hostile activities endanger our region and beyond, and we expect the Security Council to take concrete and decisive action to curb this growing threat," wrote Israel's Ambassador to the United States and United Nations Gilad Erdan.
The United States and Britain said on Sunday they would work with their allies to respond to the attack.