PARIS (Reuters) -Global shares rallied on Friday, helped by signs of progress in U.S.-China trade talks, while the dollar held close to its lowest levels in more than three years.

World stock markets have rallied to record highs this week, as traders took confidence from a ceasefire between Iran and Israel and markets stepped up bets for U.S. rate cuts.

A trade agreement between the U.S. and China on Thursday on how to expedite rare earth shipments to the U.S. was also seen by markets as a positive sign, amid efforts to end the tariff war between the world's two biggest economies.

Asian shares hit their highest in more than three years in early trading, and U.S. stock futures pointed to a firm start for Wall Street shares.

The pan-European STOXX 600 index was up 0.8% on the day, set for a 1.1% weekly gain - its best week since mid-May.

London's FTSE 100 was up 0.5% and Germany's DAX gained 0.6%.

The MSCI World Equity Index touched a fresh record high and was set for a weekly gain of 2.8%.

The S&P 500 index is up just 4.4% this year overall, following a volatile first half of the year, dominated by U.S. President Donald Trump's "Liberation Day" tariff announcement on April 2, which sent stocks plunging.

"What we are having right now is potentially some optimism about some trade deals," said Vasileios Gkionakis, senior economist and strategist at Aviva Investors.

"We have... come from quite low levels in the aftermath of the Liberation Day in April. To a certain extent we have also had some mini-selloff on the back of the events in the Middle East, and in that sense we're rebounding."

Trump has set July 9 as the deadline for the European Union and other countries to reach a deal to reduce tariffs.

Mark Haefele, Chief Investment Officer at UBS Global Wealth Management said that in the near-term, the firm saw greater upside potential in U.S. and emerging markets than in Europe.

DOLLAR DROP

The dollar remained on the backfoot, hovering near its lowest level in 3-1/2 years against the euro and sterling.

The dollar index was down a touch on the day at 97.269, holding near its lowest in more than three years. The euro was at $1.1708, getting a lift after data showed French consumer prices rose more than expected in June.

It held near multi-year peaks hit a day earlier.

"We see the U.S. dollar as unattractive," said Haefele at UBS Wealth Management.

Markets are focused on U.S. monetary policy, as traders weigh up the possibility of Trump announcing a new, more dovish chair of the Federal Reserve.

Traders have stepped up their bets on U.S. rate cuts, and are now pricing in 64 basis points (bps) of easing this year versus 46 bps expected on Friday.

The dollar is having its worst start to a year since the era of free-floating currencies began in the early 1970s.

"I don't think it's just the repricing of the Fed, I think there is a broader issue here of some tarnishing of U.S. exceptionalism," Aviva Investors' Gkionakis said.

Core PCE price data, the U.S. central bank's preferred measure of inflation, is due later in the session.

German 30-year government bond yields were on track for their biggest weekly increase in nearly four months after rising this week on expectations of increased borrowing by Germany's government.

Oil prices meanwhile rose but were set for their steepest weekly decline since March 2023, as the absence of significant supply disruption from the Iran-Israel conflict saw any risk premium evaporate.

Brent crude futures rose 0.5% to $68.06 a barrel while U.S. West Texas Intermediate crude was up by the same amount to $65.54.