While Wall Street ended with more tech-led records, traders took a breather in Asia following a recent strong run-up, with attention also turning to the release of US jobs data at the end of the week.
The US president said he had held talks with the Israeli prime minister and a "very good call" through unnamed representatives with the Hezbollah militant group.
A post on Trump's official Truth Social account said Netanyahu agreed to call off a military raid on Beirut while the Lebanon-based group said "all shooting will stop".
Lebanon's US embassy said Hezbollah had accepted a US proposal for a "mutual cessation of attacks".
But the Israeli leader appeared to cast doubt on any truce, while a report in the US news outlet Axios said Trump called him "crazy" and accused him of putting Iran peace talks at risk.
In a separate post, the president said "talks are continuing, at a rapid pace, with the Islamic Republic of Iran. Thank you for your attention to this matter!"
But Iran's news agency Tasnim reported Tehran had suspended dialogue with mediators in protest of Israel's expanding offensive in Lebanon against Iran's ally Hezbollah.
In a message carried by state TV, the Revolutionary Guards intelligence body said "crossing the red lines in Lebanon and Gaza" would mean "direct war".
Tasnim reported that Iran would keep a block on the Strait of Hormuz -- through which about a fifth of global oil passes -- and, with its allies, "activate other fronts", including the Bab al-Mandab Strait at the entrance of the Red Sea.
Earlier Monday, the US leader had told CNBC that "I don't care" if the Iran peace talks collapsed, adding that "frankly, I thought they started to get very boring".
Iran's comments sent oil prices surging as much as seven percent Monday before they pared the gains. Both main contracts were down Tuesday.
With uncertainty continuing to hang over the crisis, Asian equity traders moved cautiously after a healthy, tech-fuelled run-up that has pushed some markets to record highs.
Seoul, which has been at the forefront of the rally this year, dropped almost two percent, while Tokyo was off more than one percent, having also hit fresh new peaks.
Shanghai, Sydney and Wellington were down, though there were gains in Hong Kong, Singapore, Taipei, Manila and Jakarta.
That came on the back of records for all three main indexes on Wall Street that came as chip titan Nvidia rocketed more than six percent after unveiling a powerful laptop chip for Windows machines.
Traders are also awaiting the release of key US jobs figures on Friday, which should provide a fresh snapshot of the US economy as rising energy prices sends inflation rising.
They will also be the first under new Federal Reserve boss Kevin Warsh after he last month replaced Jerome Powell, who was constantly rebuked by Trump for not cutting interest rates enough.
- Key figures at around 0230 GMT -
West Texas Intermediate: DOWN 0.6 percent at $91.62 a barrel
Brent North Sea Crude: DOWN 0.5 percent at $94.51 a barrel
Tokyo - Nikkei 225: DOWN 1.6 percent at 65,833.49 (break)
Hong Kong - Hang Seng Index: UP 1.5 percent at 25,770.83
Shanghai - Composite: DOWN 0.1 percent at 4,054.80
Euro/dollar: UP at $1.1633 from $1.1632 on Monday
Pound/dollar: DOWN at $1.3455 from $1.3458
Dollar/yen: UP at 159.69 yen from 159.67 yen
Euro/pound: UP at 86.46 pence at from 86.43 pence
New York - DOW: UP 0.1 percent at 51,078.88 (close)
London - FTSE 100: DOWN 0.7 percent at 10,338.95 (close)
dan/ane