The IBEX 35 opened Tuesday with a modest rebound, still gripped by fears of a prolonged conflict in the Middle East, jitters over stretched valuations in tech stocks, and the prospect of higher interest rates.

Following the previous session's decline, sentiment improved slightly after Iran and Israel announced a suspension of mutual attacks on Monday, news that helped ease oil prices.

The truce followed a call from US President Donald Trump for both countries to halt hostilities, although Tehran warned it would resume strikes if Israel continues to bomb Hezbollah in Lebanon.

The wave of attacks over the last twenty-four hours marked the most direct confrontation between Iran and Israel since the April ceasefire, threatening to derail Washington's efforts to reach an agreement with Tehran to end a war that has lasted more than three months.

In parallel, the rally in bond yields continued to test already strained equity valuations, in a context where maritime traffic through the Strait of Hormuz remains severely restricted as a result of the war in the Middle East.

Friday's robust US employment figures led the market to increase bets on further hikes in borrowing costs this year, pending US consumer price data to be published on Wednesday, which is expected to confirm that energy costs continued to push headline inflation higher in May.

Futures are pricing in approximately a 60% probability of a rate hike by the Federal Reserve as early as October, while a quarter-point increase is almost fully priced in for December.

Markets also take for granted a 25 basis point hike to 2.25% by the European Central Bank at its meeting on Thursday, and place the benchmark rate at 2.5% or 2.75% by year-end.

In the tech sector, bargain hunting in semiconductor stocks temporarily warded off anxiety in a sector that has suffered a correction in recent days, amid fears that the runaway rally linked to artificial intelligence may have gone too far and created a bubble on the verge of bursting.

In this regard, traders were analyzing the latest developments in the sector after OpenAI, the creator of ChatGPT, confidentially filed documents for its US initial public offering on Monday, joining its rival Anthropic in a multi-billion dollar race to secure funding in the capital markets.

'(...) the filing of the prospectus for Open AI's IPO could boost tech/semis and leave a better balance in the US than in Europe', Bankinter analysts noted in their pre-opening note. 'If geopolitics allow, it will be the most important news of the session', added these experts, who, in any case, predicted a broadly sideways session.

The next major test for the tech sector will come with Oracle's results on Wednesday and Adobe's the following day.

Investors will also be watching the massive SpaceX IPO, which is expected to be priced on Thursday to begin trading on Friday.

Against this backdrop, at 0702 GMT on Tuesday, the Spanish benchmark IBEX 35 was up 24.80 points, or 0.14%, at 18,247.90 points, while the FTSE Eurofirst 300 index of leading European shares was down 0.08%.

In the banking sector, Santander rose 0.66%, BBVA gained 0.41%, Caixabank advanced 0.53%, Sabadell fell 0.03%, Bankinter appreciated 0.32%, and Unicaja Banco rose 0.50%.

Among the large-cap non-financial stocks, Telefónica fell 0.23%, Inditex shed 0.18%, Iberdrola lost 0.23%, Cellnex dropped 0.35%, and the oil company Repsol rose 0.17%.

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