* North Korea rhetoric drives safe haven currencies
* European stocks recover as jitters subside
* Euro zone businesses report strong Q3 activity
* All eyes on PM May as Florence speech awaited
* Brexit bellwether sterling holds firm
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh (Recasts, updates prices)
By Helen Reid
LONDON, Sept 22 (Reuters) - Jitters over a fresh exchange of barbs between North Korea and the United States eased in Europe on Friday as strong economic data supported European stocks, and investors' focus turned to a planned speech by Britain's prime minister on Brexit.
Europe's main stock index recovered from early losses following a sell-off in Asian stocks and a rush to safe-haven currencies after North Korea said it might test a hydrogen bomb in the Pacific Ocean.
Risk aversion drove investors into the Swiss franc and Japanese yen, with the Swiss currency up 0.3 percent to 0.9681 francs per dollar, while the yen firmed 0.5 percent. Safe-haven gold rose 0.4 percent.
European benchmarks swung into positive territory, though the mining sector still showed signs of strain as metals prices were battered by the heightened geopolitical risk in Asia.
U.S. stock futures indicated a 0.2 percent fall for the S&P 500, though markets were showing growing signs of fatigue over the belligerent U.S.-North Korea rhetoric.
"North Korea poses such a binary risk that it's very hard to price, and at the moment investors just have to look through it," said Mike Bell, global market strategist at JP Morgan Asset Management.
European investors were shifting focus from North Korea to a keenly anticipated speech by British Prime Minister Theresa May in Florence, in which she was expected to update her vision of the Brexit negotiations.
Brexit bellwether sterling hovered at a two-month high against the euro, having firmed against both euro and dollar this week as traders anticipated May would strike a softer tone on negotiations for Britain's exit from the EU.
"Sterling's rally in the past couple of weeks is partly in reaction to the Bank of England but also reflects an assumption that it's more likely we do get a transitional deal," said Mike Bell, global market strategist at JP Morgan Asset Management.
"If that's what May is laying out today that would be supportive, but I think you have seen a lot of that move priced in already," he added.
Options markets were pricing a large GBP/USD reaction to the speech, as investors bought protection against sharp fluctuations.
Euro zone businesses ended the third quarter with much stronger growth than predicted, PMI surveys showed, adding to evidence of the region's newfound dynamism which has spurred strong inflows into European equities this year.
"This encouraging economic backdrop is strengthening the EU governments' optimism about the future, helping to reinforce their firm stance vis a vis the UK in the Brexit negotiations," said Societe Generale cross-asset strategists.
The euro gained 0.4 percent to $1.1989, on track to end the week higher.
The dollar index against a basket of six major currencies was down 0.4 percent at 91.86.
Crude oil prices steadied as ministers from the Organization of the Petroleum Exporting Countries, Russia and other producers geared up to meet later on Friday to discuss a possible extension of supply cuts.
Brent crude hovered after hitting a five-month high at $56.63 a barrel.
The 10-year Treasury yield declined about 2 basis points to 2.255 percent as risk aversion favoured government bonds. It had risen for nine consecutive sessions prior, brushing a six-week high of 2.289 percent.
German bond yields hardly budged ahead of elections on Sunday which market participants said would yield no big surprises with Chancellor Merkel likely to win a fourth term.
MSCI's world equity index, which tracks shares in 46 countries, remained on track to eke out a weekly gain, holding near its latest record high hit on Wednesday as investors' enthusiasm for stocks showed few signs of waning.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Editing by Gareth Jones