* March job gains surpass expectations, unemployment rate dips

* ISM non-manufacturing PMI decelerates, prices paid hit 3-1/2-year high

* Soleno Therapeutics surges on Neurocrine’s $2.9 bln buyout deal (Updates to market close)

By Stephen Culp and Purvi Agarwal

April 6 (Reuters) – U.S. stocks advanced on Monday as investors looked for signs of progress toward a U.S.-Iran ceasefire deal and evaluated President Donald Trump’s progressively heated threats of escalation should Iran fail to reopen the Strait of Hormuz.

Iran has rejected the U.S. proposal for an immediate ceasefire, insisting instead on a permanent end to the war, according to the Islamic Republic News Agency (IRNA). The rejection followed Trump’s increasingly bellicose ultimatums, vowing to rain “hell” on Iran if the crucial Strait of Hormuz bottleneck remains closed to oil tanker traffic.

Investors drew some reassurance from a report that indicated the U.S., Iran and a group of regional mediators continued to discuss terms of a potential ceasefire.

All three major U.S. indexes advanced slightly, with the S&P 500 and the Nasdaq on track for the fourth consecutive day of gains.

“The reality is we’re inching, hopefully, closer to some type of resolution,” said Ryan Detrick, chief market strategist at Carson Group in Omaha. “Unfortunately, it’s not going to be today. But I think investors are feeling like we’re seeing more talking on each side.”

“The day-to-day volatility and headlines can be rather nauseating,” Detrick added. “But there’s a sense of optimism in the air with this upcoming earnings season, which starts very soon, that corporate America once again will show solid, solid performance and likely justifying what we still think is a bull market.”

The U.S. war on Iran has roiled markets for a little over a month. Spiking crude prices stoked inflation fears, and stocks have tumbled. Even though the S&P was on track for its fourth consecutive session of gains, the bellwether index remains down about 4% since the conflict began.

Economic data on Monday showed the U.S. services sector expanded at a slower-than-expected pace in March, even as employment contracted in the sector and prices paid, an inflation predictor, surged to its highest level since October 2022.

The much-anticipated March jobs report, released on the Good Friday market holiday, showed the U.S. economy added 178,000 jobs last month, nearly triple the 60,000 consensus, an upside surprise dampened by a revision of February’s job losses, to 133,000 from 92,000.

According to preliminary data, the S&P 500 gained 29.02 points, or 0.44%, to end at 6,611.71 points, while the Nasdaq Composite gained 114.29 points, or 0.52%, to 21,993.47. The Dow Jones Industrial Average rose 170.36 points, or 0.37%, to 46,675.03.

Trading volumes on Monday were thin, as many markets in Europe and Asia are closed for public holidays.

Shares of Soleno Therapeutics jumped after Neurocrine Biosciences agreed to acquire the rare-disease drugmaker for $2.9 billion in cash.

Rising bitcoin prices boosted cryptocurrency firms Coinbase and Strategy.

(Reporting by Stephen Culp; Additional reporting by Purvi Agarwal and Avinash P in Bengaluru; Editing by David Gregorio)