European shares rise to 15-month high as reflation rally resumes

* STOXX 600 up 0.7 pct to 15-mth high

* Lufthansa (Xetra: LHAB.DE - news) touches one-year high after results

* Fed rate hike boosts miners, banks

* Anglo American (LSE: AAL.L - news) tops STOXX after billionaire buys stake

* Renault (LSE: 0NQF.L - news) drops as CEO targeted in diesel probe (ADVISORY- Follow European and UK stock markets in real time on the Reuters Live Markets blog on Eikon - see cpurl://apps.cp./cms/?pageId=livemarkets)

By Helen Reid

LONDON, March 16 (Reuters) - European shares hit their highest level in 15 months on Thursday, with basic resource and banking stocks rising after the U.S. Fed raised rates and centre-right Prime Minister Mark Rutte won elections in the Netherlands.

The pan-European STOXX 600 index hit its highest level since December 2015, last up 0.6 percent.

Amsterdam's AEX index hit its highest level in more than nine years, up 0.7 percent, while both Germany's DAX and France's CAC 40 hit their highest levels since mid-2015.

Dutch PM Rutte fought off the challenge of anti-Islam and anti-EU rival Geert Wilders to score an election victory that was hailed across Europe by governments facing a rising wave of nationalism.

But Arne Petimezas, analyst at AFS Group in Amsterdam, said Dutch markets were already out-performing on Wednesday, and rising shares were mainly driven by the Fed's dovish tone.

"The rate hike that the US Federal Reserve administered yesterday has been the more dominant factor in financial markets, lifting both bonds and stocks," said Lukas Daalder, chief investment officer at Robeco Investment Solutions.

Basic resource stocks were boosted by the sharp fall of the dollar against major currencies on Wednesday on the Fed's more gradual pace of monetary tightening.

Anglo American was the top European gainer after Indian billionaire and Vedanta Resources (Other OTC: VDNRF - news) majority shareholder Anil Agarwal said he would buy a stake of up to 2 billion pounds in the miner, making his Volcan Trust the second-biggest shareholder after South Africa's Public Investment Corp.

Anglo led Europe's basic resource stocks higher, the top sectoral gainers, up 3.5 percent.

Antofagasta (Other OTC: ANFGF - news) , Fresnillo (Frankfurt: A0MVZE - news) , BHP Billiton (NYSE: BBL - news) and Randgold Resources were up 5.7 to 6.7 percent.

The Fed's rate hike also raised banking stocks, which gained 1.3 percent, with Banco Santander (Amsterdam: 817651.AS - news) the best performer.

Results also boosted some companies' stocks.

Lufthansa gained 5.1 percent after its results. The German airline posted an improved net debt position and set a brighter outlook, saying it expected profits to fall only slightly despite lower fares and a rising fuel bill.

Italian insurer Generali (EUREX: 566030.EX - news) rose 3 percent after it pledged a higher dividend after posting its best profit in nine years.

"The beat looks to be good quality and is well spread by division with life up 18 percent y/y and non-life up 13 percent y/y," said UBS (LSE: 0QNR.L - news) analysts.

Generali said it was confident in a future as an independent company, after Italy's largest bank Intesa Sanpaolo (Amsterdam: IO6.AS - news) scrapped its bid to take over the insurer.

Renault was the top faller, down 3.8 percent after the French carmaker's CEO Carlos Ghosn was targeted in a French diesel cheating probe. (Reporting by Helen Reid, Editing by Vikram Subhedar)