The IBEX 35 opened higher on Tuesday, buoyed by a resurgence of cautious optimism regarding peace talks between the United States and Iran, following a decline in the previous session triggered by speculation to the contrary.

High volatility continues to dictate market direction amid fluctuating reports on negotiations to halt the conflict between Washington and Tehran, alongside Israel's confrontation with Hezbollah. During Tuesday's session, investors appeared to look past doubts over the stability of the Middle East ceasefire, instead riding a wave of optimism surrounding artificial intelligence stocks.

U.S. President Donald Trump asserted on Monday that talks with Iran remained ongoing, despite reports suggesting Tehran had suspended indirect negotiations with Washington to end hostilities in response to Israel's military escalation in Lebanon.

Late Monday, Lebanon announced a partial ceasefire between Hezbollah and Israel, signaling a limited de-escalation of a conflict that has claimed thousands of lives and weighed heavily on US-Iran talks.

Following Trump's comments and the pause between Israel and Hezbollah, Brent crude fell 0.9% to 94.13 dollars per barrel.

On the corporate front, artificial intelligence once again took center stage. AI developer Anthropic announced it had confidentially filed for a U.S. initial public offering, a move that could command a valuation of one trillion dollars. Meanwhile, Alphabet announced plans to raise 80 billion dollars through equity issuance to accelerate the expansion of its AI infrastructure.

Regarding macroeconomic data, the session will be highlighted by the release of the Eurozone's May CPI figures.

Analysts at Bankinter noted that, following indicators from several bloc members, 'it seems to be understood that inflation peaks will be lower than initially estimated at the start of the conflict and that, for now, inflation is not permeating the economy via second-round effects.'

'All of this provides the ECB with room for maneuver and makes us somewhat skeptical regarding the rate hike next week currently priced in by the market,' they added.

In any event, the market remains focused on Friday's U.S. jobs report, which could provide clues on the Federal Reserve's next moves. According to Bankinter analysts, the institution 'is in a comfortable position to 'wait and see''.

As of 0700 GMT, Spain's benchmark IBEX 35 was up 118.50 points, or 0.65%, at 18,303.40 points, while the FTSE Eurofirst 300 index of leading European shares advanced 0.44%.

In the banking sector, Santander rose 0.68%, BBVA gained 1.29%, Caixabank advanced 0.99%, Sabadell climbed 0.88%, Bankinter added 0.91%, and Unicaja Banco rose 1.06%.

Among non-financial heavyweights, Telefónica edged up 0.03%, Inditex advanced 0.46%, Iberdrola gained 0.05%, Cellnex rose 0.71%, and oil major Repsol fell 1.41%.

(Reporting by Tomás Cobos; editing by Benjamín Mejías Valencia)