03:57 PM EDT, 06/02/2026 (MT Newswires) -- US equity indexes traded mixed amid conflicting reports of the status of peace talks between Washington and Tehran, while parts of Lebanon are rumored to remain under Israeli attack.

The Nasdaq Composite was little changed at 27,082.2, giving up intraday gains ahead of the close on Tuesday. The S&P 500 edged up 0.1% to 7,610.3, and the Dow Jones Industrial Average climbed 0.5% to 51,352.6.

Iran stopped communicating with mediators about extending a ceasefire in the war with the US and Israel, two semiofficial Iranian news agencies reported Tuesday, but President Donald Trump disputed the claim and said talks were continuing, according to the Associated Press.

CNN, however, reported that Iranian media outlets have signaled talks between Tehran and Washington are ongoing, a day after reports that Iran suspended them. The country's top negotiator has threatened escalation if Israel's attacks on Lebanon continue, the news report added.

Washington won't remove sanctions on Iran in exchange for a full reopening of Hormuz, adding that any sanctions relief is conditioned on Iran giving up enriched uranium, Al Jazeera cited US Secretary of State Marco Rubio as saying on Tuesday at a Senate hearing.

The fourth round of talks between Israel and Lebanon is underway in Washington, DC, where Lebanese negotiators hope to secure a halt to attacks on and occupation of the south, Al Jazeera reported on the same day. The Israeli army has carried out several attacks on the southern Lebanese Nabatieh governorate, the news report added.

Brent crude futures climbed 1% to $95.94, and West Texas Intermediate crude oil futures jumped 1.5% to $93.51. Both crude types were lower by more than 1% each earlier in the session.

Shares of Hewlett Packard Enterprise ( HPE ) surged nearly 19%, the top gainer on the S&P 500, after the tech giant reported fiscal Q2 earnings ahead of analysts' forecasts.

Marvell Technology's ( MRVL ) shares soared 30%, the biggest outperformer on the Nasdaq, after multiple news outlets reported that Nvidia ( NVDA ) chief executive officer Jensen Huang called the chipmaker the next "trillion-dollar company."