Europe's index of 300 leading shares, which posted its biggest gain in two months on Monday, closed 0.3 percent higher.
The Mexican peso, which strengthened as the perceived chances of an election victory by Republican Donald Trump ebbed, retained its solid gains from Monday.
"As markets head into the USA election, a final recalibration of risk is in train", Michael McCarthy, chief market strategist at CMC Markets in Sydney, wrote in a note.
Ms. Clinton's chances of winning got a boost on Sunday when the US Federal Bureau of Investigation said it stood by its July finding that the democratic candidate was not guilty of criminal wrongdoing in her use of a private email server.
"While the market is broadly pricing in a Clinton victory, we are well away from the final results", said Ipek Ozkardeskaya, senior market analyst at London Capital Group.
Against a basket of currencies, the dollar was up 0.2 percent at 97.935 .DXY .
Clinton is generally seen by investors as offering greater certainty and stability, and, until stumbling last week after FBI Director James Comey said the agency was reviewing newly discovered emails, had been seen as the clear favourite.
"For example, we think the S&P 500 would fall below 2,000, compared to a current level of around 2,130".
While polls last week showed Mr. Trump closing in on Ms. Clinton's lead, at least five major polls on Monday showed Clinton still ahead. But investors were still mindful of the precedent of Britain's referendum on European Union membership in June, which confounded the polls by delivering a shock vote for Brexit. China's yuan eased on Tuesday after the central bank set another weaker midpoint to reflect global dollar strength, but trade was cautious ahead of the USA presidential election. The S&P 500 gained 0.38 percent and the Nasdaq 0.53 percent.
Much of the action was in the currency markets where the Mexican peso has become a touchstone for sentiment on the election as Trump's trade policies are seen as damaging to its export-heavy economy.The dollar rose 0.6 percent on the peso MXN=D2 as the early results were reported, after hitting its lowest in two months overnight.The dollar backtracked 0.3 percent on the safe haven yen to 104.80 yen JPY=, while the euro EUR= rose to $1.1031.
The Mexican currency has been a market proxy for sentiment over the USA election and has performed in inverse correlation with Republican candidate Donald Trump's perceived chances of winning the White House.
The Canadian dollar added 0.2 percent against its US counterpart and the Mexican peso rose more than 1 percent against the greenback, touching its highest since September 8. The Australian dollar gave back some of its overnight gains after rising 0.7 percent on Monday, its biggest daily percentage gain since October 19.
Crude oil futures, which rose on the revival of risk appetite on Monday, retained their gains.
"Historically, since 1927 US total share returns have been strongest at an average 16.7 percent per year when there has been a Democrat president and Republican control of the House, the Senate or both".
As some caution returned after Monday's exuberance, gold climbed 0.1 percent to $1,283 an ounce, erasing some of its 1.7 percent loss from the previous session.