(Sharecast News) - European shares rallied and oil prices fell on Tuesday as Iran and Israel agreed a ceasefire and US President Donald Trump once again claimed a peace deal with Tehran was close.

The pan-regional Stoxx 600 index was up 0.15% to 622 at 0813 BST.

Sentiment was also boosted by news that US artificial intelligence company OpenAI had secretly filed a prospectus for a potential US listing, although it gave no indication of how much money it was trying to raise.

Brent crude prices fell to $93 a barrel after Trump said talks on a peace deal with Iran were in their "final throes of what will be a very, very good deal".

When asked whether it would be matter of days or weeks, Trump claimed an agreement would take "two or three days", adding that the strait of Hormuz would "open up right away" once it was signed.

Iran on Monday stopped missile strikes against Israel but warned they would resume if Israeli forces continued their attacks on Lebanon, Tehran's foreign ministry told CNBC on Monday.

The fragility of the "peace" was highlighted by later comments from Israeli Prime Minister Benjamin Netanyahu who said the conflict with Iran and Hezbollah was "not yet over".

In equity news, shares in BE Semiconductor and Infineon both gained on the OpenAI prospectus filing.

Reporting by Frank Prenesti for Sharecast.com