WASHINGTON, April 3 (Reuters) - U.S. job growth rebounded more than expected in March as a strike by healthcare workers ended and temperatures warmed up, and the unemployment rate fell to 4.3%, but downside risks to the labor market are mounting from a war with Iran that has no clear end in sight.

Nonfarm payrolls increased by 178,000 jobs last month after a downwardly revised 133,000 drop in February, the Labor Department's Bureau of Labor Statistics said in its closely watched employment report on Friday. Economists polled by Reuters had forecast payrolls rising by 60,000 jobs after a previously reported 92,000 decrease in February.

Estimates ranged from a loss of 25,000 positions to a gain of 125,000 jobs. The unemployment rate was at 4.4% in February.

The labor market has been buffeted by uncertainty, starting with President Donald Trump's aggressive import tariffs. Just as some of the clouds were starting to clear, the U.S. Supreme Court in February struck down the duties, which Trump had pursued under a law meant for use in national emergencies.

Trump, however, responded by imposing a global tariff for up to 150 days. Data from the BLS this week showed job openings decreased by the most in nearly 1-1/2 years in February, pointing to slipping labor demand.

At the end of February, the U.S. and Israel launched strikes against Iran, sending global oil prices soaring more than 50%, and boosting domestic gasoline prices. Economists said the war, now in its second month, was another layer of uncertainty for businesses, and they expected a hit on the labor market in the just-started second quarter.

Mass deportations by the Trump administration have also contributed to labor market paralysis, economists said, by reducing supply, which ultimately hurts demand for goods and services, and workers.

Historically low labor supply growth means less than 50,000 jobs per month were needed to keep up with growth in the working-age population, economists estimated. Some estimates have put the break-even rate at zero or even negative.

Economists at JPMorgan cautioned that "negative payroll readings in any given month will become more common," adding that "even with job growth sufficient to stabilize the unemployment rate, there could be negative payroll readings at least a third of the time."

While March was probably too early to capture the fallout from the Middle East conflict, some economists said that could become evident as soon as April's employment report. The national average retail gasoline price this week topped $4 a gallon for the first time in more than three years. 

This will feed through to higher inflation and erode households' purchasing power, offsetting some of the strength in wage growth, and slowing spending. The war wiped off about $3.2 trillion from the stock market in March. Trump on Wednesday vowed more aggressive strikes on Iran. 

March's employment report likely has no impact on the interest rate outlook, with the effects of supply chain disruptions from the conflict still to work their way through the economy. The odds of a rate cut this year have greatly diminished. The Federal Reserve left its benchmark overnight interest rate in the 3.50%-to-3.75% range last month.