Without further missiles or nuclear tests from North Korea, safe haven assets' demand decreased since the beginning of the week.
The S&P 500 rose 1.1 percent to mark its biggest gain since late April and the Nasdaq Composite also climbed 1.1 percent to close just below the record closing high it set on September 1 while the Dow rallied 1.2 percent.
IG's opening calls suggest that the FTSE 100 will start the day 0.20 percent higher at 7,428 points.
CURRENCIES: The euro was down 0.2 percent at $1.1930 while the dollar rose 0.4 percent to 109.83 yen.
The financial sector.SPSY was the S&P 500's biggest driver as bank stocks were helped by rising U.S. Treasury yields, while utilities and real estate stocks were out of favour. Travelers Companies climbed 2.3% and was one of the biggest boosts to the Dow, while Progressive was up 2.2%.
Irma was a Category 5 storm when it battered Cuba but weakened to Category 1 after hitting Florida.
NORTH KOREA: Tensions between the US and North Korea have been on investors' minds recently, but North Koreans observed the 69th anniversary of the country's founding, but did not test another intercontinental ballistic missile, as South Korea's government had warned it might.
Another market focus on Tuesday will be the launch of Apple Inc's iPhone 8 as its sales will have repercussions beyond Apple for many suppliers as well as its rivals. Shares of Equifax continued to drop in the wake of news that the company suffered a cyberattack in which hackers stole sensitive information, such as social security numbers, of 143 million Americans.
The Australian dollar was 0.2 percent lower at $0.8015, extending its retreat from a two-year peak of $0.8125 scaled on Friday.
Global stock markets remained firm Tuesday as fears over an escalation in tensions between the USA and North Korea continued to subside even though the United Nations slapped further sanctions on Pyongyang. Strength in the dollar and US equities also pressured prices for the metal. On the Nasdaq, 1,775 issues rose and 1,026 fell.
ENERGY: Benchmark U.S. crude rose 16 cents to $48.23 a barrel, while Brent crude, used to price worldwide oils, was up 26 cents to $54.10 a barrel in London. Energy stocks also lost ground despite a more than 1 percent increase in crude oil prices overnight.
Japanese shares hit their highest level in a month as a weaker yen bolstered exporters and financials also gained ground in the wake of sharp gains in USA bond yields and lower-than-expected damage from Hurricane Irma. Tuesday's lone economic report - the Job Openings and Labor Turnover Survey (JOLTS) for July will be released at 10:00 ET. The benchmark 10-yr climbed six basis points to 2.12% after falling to its lowest level since November on Thursday.