European stocks advanced on Tuesday after a muted start, with the STOXX 50 rising 0.4% and the STOXX 600 up 0.3%. Sentiment improved as oil prices declined, supported by renewed optimism over a diplomatic resolution to the conflict with Iran. Kyodo News reported that Tehran has proposed reopening the Strait of Hormuz within seven days of the blockade being lifted, potentially laying the groundwork for talks during the UN General Assembly. US President Trump is scheduled to address the assembly in New York and may meet Iranian President Masoud Pezeshkian on its sidelines. Software and retail stocks were among the session’s strongest performers.