Oil prices were buoyed after a cyber attack shut down a U.S. pipeline operator that supplies nearly half of the U.S. East coast's fuel.
Europe's STOXX 600 index also reached a new historic peak after turning flat on the day, while MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.6%.
S&P 500 futures were up 0.1% while Nasdaq futures fell 0.3%.
U.S. nonfarm payrolls data on Friday showed jobs growth slowed much more than expected in April, a shock release that gave equities a lift but applied downward pressure on the dollar and U.S. Treasury yields.
"A statistical fluke and/or a temporary pause in labor market demand is the likeliest culprit for this report. However, the Federal Reserve cannot afford to adjust policy without concrete proof of a stronger labor market recovery," said Natixis economist Troy Ludtka.
On Friday the Dow Jones Industrial Average .DJI and the S&P 500 .SPX rose to record closing highs as the disappointing data on the U.S. jobs market eased concerns about a spike in consumer prices.
In recent weeks, some investors had been placing bets that a robust U.S. economic recovery from the coronavirus pandemic would force the Fed to tighten policy earlier than the central bank has outlined.
However, the weak nonfarm payrolls report caused a rapid reversal in some of these trades, which rippled through stocks, bonds and major currencies.
U.S. President Joe Biden said after the report that the figures showed the economy was not at risk of overheating and underscored how vital his administration's economic actions are.
"In the end, it is the best of all possible worlds for equities: robust economy, strong earnings, but no monetary policy tightening and more fiscal spending coming," said Giuseppe Sersale, fund manager at Anthilia in Milan.
The focus now shifts to U.S. consumer price data due on Wednesday, which will help investors determine whether they need to scale back their inflation expectations even further.
The dollar index against a basket of six major currencies was little changed at 90.136, just above 2-1/2 month lows hit earlier in the session.
The pound broke above the key $1.40 level for the first time in more than two months, even as pro-independence parties in Scottish elections won a majority.
The pound was up 0.75% against the dollar at $1.4095.
In the cryptocurrency market, ether rose to a fresh record above $4,000 and was last up 3%. Bigger rival bitcoin fell 0.9% to $57,794.
The yield on benchmark 10-year Treasury notes was little changed at around 1.575% after having plunged to a two-month low of 1.469% on Friday.
Three-month copper on the London Metal Exchange climbed to an all-time high of $10,747.50 a tonne after first breaking through a decade-old record on Friday.
Copper also hit a record high on the Shanghai Futures Exchange as the most-traded June copper contract closed up 4.8% to 77,720 yuan ($12,094.62) a tonne.
Analysts said Friday's disappointing April non-farm payrolls further fuelled the rally in metal prices as the dollar got hit.
Brent crude rose 0.75% to $68.79 per barrel as the disruption to U.S. supplies rattled energy markets, while U.S. crude added 0.6% to $65.31 a barrel.
The White House was working closely with top U.S. fuel pipeline operator Colonial Pipeline on Sunday to help it recover from the ransomware attack that forced the company to shut its main fuel lines.
(Reporting by Danilo Masoni in Milan and Stanley White in Tokyo; editing by Emelia Sithole-Matarise and Mark Heinrich) ((Danilo.Masoni@TR.com; +39-02-66129734; Reuters Messaging: email@example.com; On Twitter https://twitter.com/damasoni))