The US benchmark S&P 500 stock index set record intra-day and closing highs on Monday as last week's strong monthly US jobs report worked its way into financial markets, and European shares rose as a single candidate emerged to succeed David Cameron as British prime minister.

The S&P 500 ended at a record high of 2,137.16 after touching a record intra-day high of 2,143.16. It overtook the previous highs touched in May 2015 as investors harboured greater optimism about the US economy after last Friday's stronger-than-expected jobs report.

The gains in US shares on Monday were broad-based. Industrials and consumer staples also hit record highs. The tech-heavy Nasdaq Composite rose above 5,000 for the first time since December during the session.

The STOXX Europe 600 closed up 1.6 per cent at 332.72, its highest close since Britain's vote to exit the European Union on June 23. Theresa May won the race to succeed David Cameron as Prime Minister, reducing political uncertainty in the UK.

“The markets are having a feel-good rally because the jobs report on Friday was better-than-expected and that was followed up by some good election news in Britain and Japan,” said Alan Gayle, senior investment strategist at RidgeWorth Investments in Atlanta. “Investors have been looking for a reason to buy stocks and now they have it.”

US Treasury yields rose on Japanese Prime Minister Shinzo Abe's order for a fresh round of fiscal stimulus, which reduced demand for safe-haven US bonds, and as investors braced for $56 billion in supply this week. Abe's ruling coalition clinched a victory in Sunday's election to parliament's upper house.

US 30-year yields were last at 2.146 per cent after hitting a record low of 2.089 per cent in overnight trading. Benchmark 10-year yields were last at 1.432 per cent from a yield of 1.365 per cent late Friday.

MSCI's all-country world equity index was last up 3.77 points or 0.94 per cent at 404.76.

The Dow Jones industrial average closed up 80.19 points or 0.44 per cent at 18,226.93. The S&P 500 ended up 7.26 points or 0.34 per cent at 2,137.16. The Nasdaq Composite closed up 31.88 points or 0.64 per cent at 4,988.64.

Europe's broad FTSEurofirst 300 index ended 1.5 per cent higher at 1,315.49.

Benchmark Brent crude and US crude prices hit two-month lows of $45.90 a barrel and $44.53 a barrel, respectively, on extended selling after the market's break below a key technical support level last week due to oversupply fears.

US crude settled down 65 cents at $44.76 per barrel, while Brent crude settled 51 cents lower at $46.25 a barrel.

The dollar rose to a 10-day high against the safe-haven yen of 102.89 yen, climbing more than 2 per cent, following Abe's call for more stimulus.

“It looked like part of what held the BOJ back several times earlier this year is it just didn't make sense to expand (quantitative easing) if there's no coordination with fiscal policy,” said Greg Anderson, global head of foreign exchange strategy at BMO Capital Markets in New York. “But now there is.”