Updates throughout

By Nell Mackenzie and Amanda Cooper

LONDON, July 3 (Reuters) - Global stocks headed towards their best weekly performance in two months on Friday after a lukewarm U.S. jobs report dampened expectations for an imminent rate hike from the Federal Reserve, which restrained the dollar and gave gold a boost.

In Europe, the STOXX 600 .STOXX hit another record high and was last trading up 0.6% as it headed for a weekly gain of 2.6%, its best since mid-May.

MSCI's broadest index of world shares .MIWD00000PUS rose 0.4%, set for a gain of 2% this week, the most in two months.

"Yet again, the tech-lite European indices are back in demand, even more so given that the stocks within them trade on much lower price-to-earnings than those typically seen over in the U.S. So, not only are Europe’s indices less exposed to the AI trade, but they are also relatively cheap," said David Morrison, senior market strategist at Trade Nation.

Semiconductor stocks and other AI-linked companies fell on Wall Street on Wednesday and Thursday, as investors favoured financials and healthcare shares, among others.

By Friday, chip stocks rebounded in Asia, pushing up South Korea's volatile KOSPI .KS11 by around 6% and Tokyo's Nikkei .N225 by 1.5%. Purchasing Managers' Index data released on Friday indicated increased activity across major Asian economies.

Japan's services sector returned to expansion in June after stalling the previous month. China's services activity expanded at a slightly slower pace, but overseas demand rose at the fastest rate in 20 months.

"The PMIs remain healthy by recent standards and still imply stronger economic momentum across Q2 as a whole," analysts from Capital Economics said of the Chinese data.

U.S. LABOUR MARKET COOLING

U.S. job growth slowed sharply in June and payroll gains for the prior two months were revised lower, according to data released on Thursday, pointing to a cooling labour market.

The tepid jobs data doused traders' expectations of an imminent rate hike and raised the chances that the Fed will keep rates on hold until October.

Fed funds futures are pricing an implied 46.8% probability that the U.S. central bank will keep rates steady at its September 15 to 16 meeting, compared to a 35.8% chance a day earlier, according to the CME Group's FedWatch tool.

This helped lift the gold price XAU= by 1% to above $4,160 an ounce as it headed towards its first weekly gain since the end of May, up 1.8%.

Yet inflation remained a concern.

"Our biggest anticipated risk this year, even before the Iran war, was shipping," said James Rossiter, head of global economics at TD Securities.

"Ships have been rerouted all over the world because of the Hormuz Strait closure, leading to less shipping capacity globally," he said, suggesting the price effects of this were still working their way through the global economy.

U.S. futures rose, reflecting the upbeat tone elsewhere. S&P 500 and Nasdaq futures ESc1, NQc1 were up 0.3% and 1.2% respectively. The U.S. market is closed on Friday for Independence Day.

The dollar, which has risen to its highest level in over a year against a basket of major currencies this week =USD, took a breather on Friday. The euro EUR=EBS was up 0.1% at $1.144, while the pound GBP= was steady at $1.335.

Against the yen JPY=, which hit its weakest in 40 years this week, the dollar was steady around 161. The few traders around on Friday remained on high alert for signs of official buying from authorities in Tokyo, who may have adopted a new approach to their forays into the market, according to a Reuters exclusive on Thursday.

In commodities, Brent crude oil futures LCOc1 rose 0.45% to $71.12.