Australia's S&P/ASX 200 closed down 3.40 points, or 0.04%, at 8,726.00 on Tuesday, June 2.

US Secretary of State Rubio said Iran pledged to open the Strait of Hormuz once a ceasefire took effect, but it has not.

Iran's foreign ministry on the 1st condemned continued US and Israeli violations of the ceasefire, saying any breach on any front constitutes a violation of the entire ceasefire arrangement. It reiterated the April 8 ceasefire — including its application to Lebanon — and said the US must be held responsible for its own violations and accountable for Israeli actions. The statement added Iran would, under the right of self‑defense in international law, "use all capabilities to defend its interests" if necessary.