Aug 4 (Reuters) - U.S. stocks were higher and the U.S. dollar and Treasury yields lower after a new government jobs report showed a slowing, but still tight U.S. labor market.

Nonfarm payrolls increased by 187,000 jobs last month, the Labor Department said in its closely watched employment report on Friday, slightly below expectations of 200,000 jobs. At the same time, the unemployment rate fell to 3.5% from 3.6% in June.

Randy Frederick, managing director of trading and derivatives at Charles Schwab in Austin, Texas, said the mixed jobs report "plays into the soft landing, or the no-landing, narrative that the markets have been slowly trudging higher on."

“This ought to relieve some of that concern about the fact that the economy is too strong, which would cause concern that perhaps we get another rate hike in September," Frederick added.

The Dow Jones Industrial Average rose 0.35%, to 35,338.46 and the S&P 500 gained 0.59%, to 4,528.33.

The technology-heavy Nasdaq Composite added about 1%, to 14,101.48. Two technology giants reported earnings after the market close on Thursday: Amazon showed sales growth and profit that beat analyst estimates, while Apple forecast a sales slump to continue into the current quarter.

European stock indexes fell on Friday, The STOXX 600 was down 0.2% on the day, while London's FTSE 100 was down 0.3%.

The MSCI All-World index was last up 0.16% following the job news. It had been headed for its biggest weekly drop in five months, thanks in part to a surge in government bond yields this week after more data pointed to slowing inflation and the prospect of a deluge of U.S. Treasury supply.

Economists who have long been forecasting a downturn by the fourth quarter of this year are increasingly becoming convinced that the "soft-landing" scenario for the economy envisaged by the U.S. Federal Reserve is now possible.

Data also showed the number of Americans filing new claims for unemployment benefit rose slightly last week, while layoffs dropped to an 11-month low in July as labour market conditions remained tight.

The benchmark indices closed little changed the previous day after a choppy trading session, as investors weighed up the implications of rising Treasury yields along with the latest batch of economic data and earnings.

"It’s a very fragile market," said Francesco Sandrini, head of multi-asset strategy at Amundi.

The dollar meanwhile fell 0.5% against a basket of major currencies, a reversal after two consecutive weekly gains.

It has made the most headway against some of this year's better-performing currencies, including the pound, under pressure since the Bank of England delivered a smaller rate rise than many had hoped for. Sterling was last up 0.5% on the day, still down about 0.5% in August.

China's yuan, last flat on the day, gained some respite after an official said on Friday the central bank would use policy tools flexibly to ensure reasonably ample liquidity in the banking system.

Investors have been hoping policymakers will deliver more broad-based stimulus to boost the post-pandemic recovery as the world's second-largest economy struggles with weak demand at home and abroad.

U.S. Treasury yields dropped slightly and then pared back losses, after jobs data on Friday showing the U.S. economy maintained a moderate pace of job growth in July.

The yield on 10-year Treasury notes was down 6.8 basis points to 4.121%. 30-year yields were down 2.9 basis points to 4.275%.

Rating agency Fitch this week surprised markets by stripping the United States of its prized triple-A credit rating and cited the country's deteriorating fiscal position as one of the key drivers, thrusting the government's finances into the spotlight.

Earlier in the week, the U.S. Treasury said it expects to borrow just over $1 trillion in the third quarter of this year alone, $273 billion more than its May estimate.

Oil prices headed for a sixth straight weekly gain, driven by the prospect of reduced supply from Saudi Arabia and Russia. U.S. crude rose 0.33% to $81.82 per barrel and Brent was at $85.46, up 0.38% on the day.

(Reporting by Lawrence Delevingne in Boston and Amanda Cooper and Elizabeth Howcroft in London. Additional reporting by Ankur Banerjee and Sruthi Shankar; Editing by Sharon Singleton )