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* Graphic: Global asset performance http://tmsnrt.rs/2yaDPgn

* Graphic: World FX rates http://tmsnrt.rs/2egbfVh

NEW YORK/LONDON, June 28 (Reuters) - Global equity markets edged lower on Monday, though supported by U.S. shares hitting new highs, while Treasury bond yields eased and the dollar was little changed as investors await jobs data that could sway the Federal Reserve's monetary policy.

MSCI's all country world index, which tracks shares across 50 countries, slid 0.1% as markets in Europe fell. But fresh highs by the S&P 500 and the Nasdaq offset the declines in the major French, German and UK bourses as the global index is U.S.-centric.

Weaker-than-expected U.S. inflation and news of a possible bipartisan U.S. infrastructure agreement boosted risk appetite as the week opened. The infrastructure plan is valued at $1.2 trillion over eight years, of which $579 billion is new spending.

The plan is less than the White House’s initial proposal, but the total amount is likely to be greater than Republicans' initial figure and lead Congress to spread the initiative across two bills, said Solita Marcelli, UBS’ chief investment officer for the Americas for its global wealth management division.

While that could provide a tailwind for the reflation trade, Marcelli said "(the spending) will be spread out over a multi-year period, and tax increases could be part of the mix. So the stimulative impact on markets overall may not be very large," Marcelli said.

Stock markets across the world rebounded last week, but growing concern about the spread of the Delta variant of the COVID-19 virus took some shine off on Monday.

European stocks, as measured by the pan-European STOXX 600 index, closed down an unofficial 0.53%, still near record highs. Germany's DAX fell 0.34%, while France's CAC 40 slid 0.89% and Britain's FTSE 100 index dipped 0.88%.

Travel and leisure stocks took a particular hit, with the region's sectoral index falling to a one-month low.

"In Europe, the rapid spread of the highly contagious Delta variant is looming over the start of the tourist period," said Sophie Griffiths, market analyst at OANDA. That could "be a severe blow to airlines and travel and tourism stocks, which are trading sharply lower today."

On Wall Street, the Dow Jones Industrial Average fell 175.47 points, or 0.51%, to 34,258.65, the S&P 500 gained 0.95 point, or 0.02%, to 4,281.65 and the Nasdaq Composite added 102.99 points, or 0.72 percent, to 14.463.37.

Earlier in Asia, MSCI's broadest index of Asia-Pacific shares outside Japan edge up 0.1% at 703.86. Australian shares slipped 0.1%. Japan's Nikkei and South Korea's benchmark KOPS were barely changed.

Sydney is in lockdown and Malaysia extended its lockdown due to spreading cases of the new Delta variant. Indonesia is battling record-high cases, and Thailand announced new restrictions in Bangkok and other provinces.

Chinese shares were a touch higher, with the CSI300 index up 0.2%. Data over the weekend showed profit growth at China's industrial firms slowed again in May as surging raw material prices squeezed margins and weighed on factory activity.

Investors will keep a close eye on official factory activity from China due on Wednesday. The manufacturing reading is expected to slow to 50.7 from 51. The private sector Caixin Manufacturing PMI will follow later in the week.

Oil prices slipped on Monday after hitting more than 2-1/2 year highs early in the session, hurt by the spike in COVID-19 cases in Asia ahead of this weeks OPEC+ meeting.

Brent crude was last down $1.02, or down 1.34 percent, at $75.16 a barrel. U.S. crude was last down $0.89, or down 1.2 percent, at $73.16 per barrel.

On Friday a closely watched U.S. jobs report, which could point to strong labor demand, will be released for June.

Yields for benchmark 10-year U.S. Treasuries fell on Monday, last down 5.6 basis points at 1.4799%. Last week, it notched its largest weekly gain since March.

The dollar index, which tracks the greenback versus a basket of six currencies, fell 0.016 point or 0.02%, to 91.835.

The yen was last down 0.22% at $110.5300.

An appreciating dollar took some luster off gold, with spot prices down 0.1% at $1,779.04 an ounce.

(Reporting by Ritvik Carvalho; additional reporting by Swati Pandey in Singapore; editing by Jason Neely and Chizu Nomiyama)