By Marc Jones and Stella Qiu

LONDON, July 3 (Reuters) - World shares were at a record high and the dollar firmed on Thursday ahead of key U.S. jobs data, while Europe saw Britain's bond markets steady after debt worries prompted a selloff the previous session.

A deal between the United States and Vietnam ahead of next week's worldwide U.S. trade tariff deadline provided another boost for the bulls overnight after a hectic run up in markets in recent weeks.

The pan-European STOXX 600 index .STOXX advanced 0.4%, leaving MSCI's main 47-country world shares gauge .MIWD00000PUS at its seventh record high in the last eight sessions and the dollar close to ending a four-day run of falls.

Britain's bonds clawed back some of their heavy losses spurred a day earlier by uncertainty over finance minister Rachel Reeves' future, but they remained weaker than recent levels.

The 20-year gilt yield GB20YT=RR, which is a proxy of longer term UK government borrowing costs, eased by 8 basis points after its biggest spike on Wednesday since October 2022 - during the ill-fated premiership of Liz Truss.

A tearful appearance from UK finance minister Rachel Reeves in parliament had sparked uncertainty about her future and Britain's public finances after the government was forced to ditch billions of pounds worth of welfare spending cuts.

"Some worries remain about the government being backed into a corner and losing its grip on the public finances," said Susannah Streeter, head of money and markets at broker Hargreaves Lansdown.

Focus was also on the U.S. payrolls report later which will steer ongoing debate on if and when the Federal Reserve will next cut U.S. interest rates.

Analysts are forecasting a rise of 110,000 jobs in June with the jobless rate ticking up to 4.3% but the stakes are high after a private sector payrolls report surprised with the first fall in over two years.

Traders were also waiting to see if U.S. President Donald Trump's tax and spending bill gets passed by Congress in the next 24 hours. The bill is expected to add $3.3 trillion to the United States' $36 trillion of national debt over the next decade, according to nonpartisan analysts.

Wall Street had closed on Wednesday at record highs after Trump announced that the U.S. had struck a trade deal with Vietnam, including a 20% tariff on exports to the U.S. That is lower than the 46% tariff that had been threatened, but still much higher than previous rates.

Vietnamese shares .VNI gained 0.5% to the highest since April 2022 although the local dong currency VND= hit a record low of 26,229 per dollar.

"More trade deals may soon be announced but the 20% tariff agreed with Vietnam does not augur well, and that or even higher could become the norm for some including Europe and Japan," said Shane Oliver, chief economist at AMP.

Indeed, Japan has invoked national interests as talks with the U.S. struggled, while South Korean President Lee Jae Myung said on Thursday U.S. tariff negotiations were looking difficult and he could not say if talks could conclude by next Tuesday.

MSCI's broadest index of Asia-Pacific shares .MIAP00000PUS closed up 0.3% higher. China's blue-chip index .CSI300 rose 0.6% after limp services data bolstered expectations of more stimulus, while Japan's Nikkei .N225 finished flat.

Nasdaq futures NQc1 and S&P 500 futures ESc1 were broadly flat in Europe too. .N

JOBS RISK

The dollar was hovering just above a three-year low against a basket of its major peers, up 0.1% for the day. Sterling GBP=EBS recovered 0.2% to $1.3662 after its 0.8% fall on Wednesday.

The main risk event for markets will be the U.S. payrolls figures.

The resilience of the labour market is a major reason the majority of Federal Reserve members say they can afford to hold off on cutting rates until they can gauge the real impact of tariffs on inflation.

"These labour market indicators warn of the risk that the unemployment rate could spike to 4.4%, the highest since October 2021," said Tony Sycamore, analyst at IG. "This would quickly increase the probability of a July Fed rate cut to around 70%."

Futures imply just a 25% probability for a rate cut this month from the Fed, which has not eased policy at all this year, drawing the ire of Trump who reiterated his call on Wednesday for Chair Jerome Powell to resign.

Trump, who said rates should be cut to 1% from the current Fed benchmark of 4.25% to 4.50%, has repeatedly railed against Powell for not lowering borrowing costs since his return to the White House in January.

A UBS survey on Thursday showed two in three reserve managers fear Fed independence is at risk and nearly half think the rule of law in the U.S. may deteriorate enough to influence their asset allocation significantly.

The Treasuries market was tense before the data as a weak jobs report would send yields sharply lower. Ten-year Treasury bond yields US10YT=RR slipped 3 basis points to 4.265% on Thursday, while two-year yields US2YT=RR eased 2 bps to 3.772%.

In commodities markets, oil prices were lower after jumping 3% overnight as Iran suspended cooperation with the U.N. nuclear watchdog.

Brent crude futures LCOc1 slipped 0.8% to $68.64 per barrel, while U.S. crude CLc1 was 0.7% lower on the day. O/R Gold prices =XAU also dipped, easing 0.1% to $3,352 an ounce. GOL/

(Additional reporting by Andy Bruce; Editing by Emelia Sithole-Matarise)

((marc.jones@thomsonreuters.com; +44 (0)20 7513 4042; Reuters Messaging: marc.jones.thomsonreuters.com@reuters.net X/Twitter @marcjonesrtrs))