(Adds Trump comments, updates markets)
* Nonfarm payrolls increase 224,000 in June
* Unemployment rate rises to 3.7% from 3.6%
* Average hourly earnings gain 0.2%; workweek at 34.4 hours
By Lucia Mutikani
WASHINGTON, July 5 (Reuters) - U.S. job growth rebounded strongly in June, with government payrolls surging, but persistent moderate wage gains and mounting evidence the economy was losing momentum could still encourage the Federal Reserve to cut interest rates this month.
The Labor Department's closely watched employment report on Friday suggested May's sharp slowdown in hiring was probably a fluke. Lack of concrete progress in resolving an acrimonious trade war between the United States and China, however, means the bar could be very high for the Fed not to lower borrowing costs at its July 30-31 policy meeting.
But the strong pace of job gains reduced the chances of a half percentage point rate cut at the end of the month. The U.S. central bank in June signaled it could ease monetary policy as early as this month citing low inflation and growing risks to the economy from an escalation in trade tensions between Washington and Beijing.
"We think the Fed is still on track for a 25 basis points cut given trade uncertainty and the steady downtrend in business sentiment," said Andrew Schneider, a U.S. economist at BNP Paribas Securities in New York. "An insurance cut by definition means getting ahead of a downturn, and waiting for employment to roll likely means being too late to deliver one."
Nonfarm payrolls increased by 224,000 jobs last month as government employment rose by the most in 10 months, and construction and manufacturing hiring regained speed. The economy created only 72,000 jobs in May. Economists polled by Reuters had forecast payrolls rising 160,000 in June.
Job growth averaged 172,000 per month in the first half. Hiring has cooled from an average of 223,000 jobs per month in 2018, in part as the economy runs out of workers. The pace, however, remains well above the roughly 100,000 needed to keep up with growth in the working age population.
The economy, which has expanded a record 10 years, has shifted into lower gear as the stimulus from last year's massive tax cuts and increased government spending fizzles.
The trade tensions are also dimming the economy's outlook by undercutting business confidence and leading to a downturn in equipment spending and manufacturing. Consumer spending is rising moderately and the housing market continues to struggle, while the trade deficit has widened again
President Donald Trump and Chinese President Xi Jinping last week agreed to a trade truce and a return to talks. Trump has said he is in "no hurry" to make a deal and on Wednesday accused China and Europe of "playing big currency manipulation game and pumping money into their system in order to compete with USA."
Trump on Friday said the robust employment gains indicated the United States continued to do "really, really well" and "would be like a rocket ship," if the Fed lowered rates. U.S. House of Representative Speaker Nancy Pelosi, a Democrat, welcomed the rebound in job growth, but said "hard-working Americans are still struggling under the Trump administration's disastrous special interest agenda."
The Atlanta Fed is forecasting gross domestic product rising at a 1.3% annualized rate in the April-June quarter. The economy grew at a 3.1% pace in the first quarter.
Average hourly earnings rose six cents or 0.2% in June after gaining 0.3% in May. That kept the annual increase in wages at 3.1% in June for a second straight month. The trend in wage growth has slowed from late last year when wages were rising at their fastest rate in a decade, pointing to moderate inflation.
Interest rate futures fully priced in a month-end rate cut, but dialed back expectations for an easing of 50 basis points. The dollar rose against a basket of currencies, while U.S. Treasury prices fell. Stocks on Wall Street slipped.
Fed Chairman Jerome Powell's semi-annual testimony to the U.S. Congress on the economy next week could shed light on the near-term outlook for monetary policy. The Fed in its semi-annual report to Congress on Friday repeated its pledge to "act as appropriate" to sustain economic growth.
"There is no inflationary pressure coming from the labor side," said Sung Won Sohn, an economics professor at Loyola Marymount University in Los Angeles. "It is hard to explain why wage gains are so slow in the current labor market."
The unemployment rate rose one-tenth of a percentage point to 3.7% last month as 335,000 people entered the labor market, a sign of confidence in their prospects of getting a job. Some of the recent drop in the jobless rate had been because of people leaving the labor market.
The labor force participation rate, or the proportion of working-age Americans who have a job or are looking for one, rose to 62.9% last month from 62.8% in May.
A broader measure of unemployment, which includes people who want to work but have given up searching and those working part-time because they cannot find full-time employment, rose to 7.2% in June from 7.1% in May.
Hiring picked up across nearly all sectors in June, though retail payrolls contracted for a fifth straight month, shedding another 5,800 jobs on top of the 7,300 lost in May.
Manufacturing payrolls accelerated by 17,000 jobs after rising by 3,000 in May. The surge in hiring is despite the sector struggling with an inventory bulge - concentrated in the automotive industry - trade tensions, design troubles at planemaker Boeing and slowing global growth.
Construction employment rose by 21,000 jobs last month after gaining 5,000 in May. Government payrolls rebounded by 33,000, the most since August 2018, after shedding 11,000 jobs in May. The surge in hiring was driven by local governments.
But leisure and hospitality sector payrolls increased by a moderate 8,000 in June after rising 18,000 in the prior month. Professional and business services employment gained 51,000 jobs. There were increases in healthcare and transportation and warehousing employment.
The average workweek was unchanged at 34.4 hours in June for a third straight month.
Reporting by Lucia Mutikani; Editing by Andrea Ricci