* Banks snap 3-day losing streak
* Steel stocks fall after U.S. Steel's weak forecast
* Swiss lenders gain after SNB raises negative rate threshold (Updates to close)
Sept 19 (Reuters) - European stocks rallied on Thursday as investors snapped up battered shares of eurozone banks after the U.S. Federal Reserve toned down expectations of further interest rate cuts.
The eurozone banks index, which has underperformed broader markets this year, jumped 2.4% to end a three-day run of losses while an index of eurozone stocks rose 0.6%.
Shares of Italian and Spanish banks including Bankia SA , UBI Banca and Banco Sabadell were among the top gainers on the STOXX 600 after the Fed cut rates as expected on Wednesday, but signaled there would be a higher bar to further cut in borrowing costs.
European banks, along with sectors such as miners and automakers, have gained in the recent weeks as investors rotated into cyclical sectors due to signs of easing U.S.-China trade tensions and assurances of support from major central banks.
"European banks have been lagging behind and are priced relatively cheap," said Teeuwe Mevissen, senior market economist at Rabobank.
Mevissen also said the European Central Bank's unveiling last week of a tiered rate system to mitigate the negative impact of sub-zero interest rates on banks was relief.
Spain's and Italy's indexes, which are heavily exposed to banks, outperformed the broader markets with a 1.2% and 0.8% gain, respectively.
London-listed shares rose about 0.6%, with banks leading gains after the Bank of England kept interest rates on hold as expected.
The top gainer on the STOXX 600 was Britain's online trading platform IG Group, which jumped 10.3% after it said it added more clients and saw improved trading activity in August. Rivals Plus500 and CMC Markets also rose on the news.
Clothing retailer Next PLC was the biggest decliner on the STOXX 600 after saying the first few weeks of the autumn season had been disappointing.
European steel stocks ArcelorMittal, Salzgitter , SSAB, Outokumpu and Thyssenkrupp fell between 1.6% and 4.8% after United States Steel's gloomy current-quarter earnings forecast.
Swiss shares rose 0.5% as the Swiss National Bank held its main policy rate at -0.75% and said it expected to stick to its ultra-loose monetary stance.
Shares in major lenders Credit Suisse and UBS rose more than 1% as the central bank increased the threshold above which commercial banks who park their money with the central bank have to pay negative interest.
Oslo-listed shares closed flat after Norway's central bank raised its main interest rate as expected, but said further policy tightening had become less likely. (Reporting by Sruthi Shankar in Bengaluru; editing by David Clarke)