The benchmark US S&P 500 stock index has set record closing and intraday highs for the second straight day.
This as the Dow Jones industrial average has reached record highs for the first time in over a year as optimism about the world economy and upbeat corporate results from Alcoa boosted risk appetite.
The benchmark S&P 500 ended at 2,152.14 on Tuesday, topping Monday's record close of 2,137.16, while the Dow closed at 18,347.67 to top its previous record high touched in May 2015.
The S&P 500 hit a record intraday peak of 2,155.40, while the Dow hit an intraday record of 18,371.95.
The tech-heavy Nasdaq Composite also gained, wiping out its losses for the year and notching its highest close since late December.
Alcoa reported a smaller-than-expected drop in quarterly profit, sending the aluminium producer's shares up more than 5 percent and helping boost optimism about the earnings season.
European shares rose for a fourth straight day.
Investors' appetite for equities has increased after a stronger-than-expected US jobs report for June last Friday and low yields on government bonds.
Easing political uncertainty in Britain and Japan has reduced some global uncertainties.
"Once you break convincingly above the old high, you get the momentum buying coming in," said Michael Jones, chief investment officer of RiverFront Investment Group in Richmond, Virginia.
"The better nonfarm payrolls, the better earnings glimpse that we got today with Alcoa, that says stocks are worth more, and at lower interest rates, investors are willing to pay a higher multiple."
The FTSEurofirst 300 and STOXX Europe 600 ended higher for a fourth straight session and notched their highest closes since Britain voted on June 23 to leave the European Union.
Gains in shares of Italian banks helped fuel the rise, with UniCredit ending up more than 13 percent.
MSCI's all-country world equity index was last up 0.09 points, or 0.02 percent, at 408.48.
The Dow Jones industrial average closed up 120.74 points, or 0.66 percent, at 18,347.67. The S&P 500 ended up 14.98 points, or 0.7 percent, at 2,152.14. The Nasdaq Composite closed up 34.18 points, or 0.69 percent, at 5,022.82.
Europe's broad FTSEurofirst 300 index closed up 1.14 percent, at 1,330.46.
Oil prices posted their largest daily percentage gains in more than three months, as investors' covering of short positions and a technical rebound helped lift the market off two-month lows.
Brent crude settled up $US2.22, or 4.80 percent, at $US48.47 ($A64.34) a barrel. US crude settled up $US2.04, or 4.56 percent, at $US46.80.
"The market's gotten really short over the past two weeks... and now you're seeing sudden covering," said Scott Shelton, energy futures broker with ICAP in Durham, North Carolina.
Safe-haven assets such as US Treasuries, the Japanese yen and gold fell in price. Benchmark 10-year Treasury yields, which move inversely to prices, hit a one-and-a-half-week high of 1.531 percent.
The US dollar hit its highest in more than two weeks against the yen of 104.97 yen, while gold posted its biggest one-day fall in three weeks.