* U.S., European stocks rise, Asian stocks fall
* Euro falls further on Thursday's ECB news
* European bank stocks snap rally
* Oil rises, U.S. treasury yields higher (Updates to U.S. open, changes byline, previous dateline London)
By Sinead Carew
NEW YORK, Dec 9 (Reuters) - U.S stocks followed Europe higher on Friday while the euro weakened against the dollar after the European Central Bank's Thursday decision to extend its stimulus program.
U.S. Treasury yields climbed with benchmark yields on track for a fifth straight week of increases following stronger-than-forecast Chinese inflation data and ahead of $56 billion of coupon-bearing government bond supply next week.
European shares hit their highest level since January, and were set for their best week since February, following the ECB's decision to cut monthly bond buys to 60 billion euros ($63.7 billion) from 80 billion euros and extend purchases to December - three months longer than analyst forecasts.
Stocks were helped by inflation data from China, rising prices of some commodities and general optimism after the ECB decision and before a U.S. Federal Reserve statement due out on Wednesday, according to Frances Hudson, global thematic strategist based in Edinburgh for Standard Life Investments.
"The markets are glass half-full, interpreting things in a fairly optimistic way," said Hudson.
The ECB's indication it would extend monetary support for as long as needed complemented the promise from U.S. President Elect Donald Trump of fiscal stimulus, according to analysts. But some participants said 2016 could be the high water mark for monetary easing, less than a week before the U.S. Fed is widely expected to raise over-night interest rates.
"You have to say central bank stimulus has peaked in 2016," said Charles Mackenzie, chief investment officer, fixed income, at Fidelity International.
The Dow Jones industrial average was up 47.49 points, or 0.24 percent, to 19,662.3, the S&P 500 gained 6.63 points, or 0.3 percent, to 2,252.82 and the Nasdaq Composite added 25.22 points, or 0.47 percent, to 5,442.57.
Europe's STOXX 600 was up 0.6 percent even though European bank stocks pulled back 0.4 percent. Reuters reported that the ECB had rejected a request from Italy's Monte Paschi for more time to raise cash. The continent's banking sector was still up almost 10 percent for the week, its biggest weekly jump since December 2011.
The euro dipped for a second day, after Thursday's ECB news caused its biggest daily loss against the dollar since Britain's vote to leave the European Union in June.
The euro was trading around $1.0543, down 0.7 percent against the dollar and down 1.2 percent for the week. The dollar was up 0.6 percent on the day up 0.9 percent for the week against a basket of major currencies.
MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.3 percent, though it posted a weekly gain of 1.9 percent. Japan's Nikkei ended 1.2 percent up at its highest close since December 2015.
Oil rose on growing optimism that non-OPEC producers might follow the cartel's lead by agreeing to cut output.
U.S. crude added 1.4 percent to $51.54 a barrel. Brent crude rose 0.7 percent to $54.24.
Spot gold was down 0.7 percent and was set for a weekly decline of 1.2 percent, pressured by the stronger U.S. dollar and expectations of a Fed rate hike. (Additional reporting by Abhinav Ramnarayan; Editing by Mark Trevelyan and Nick Zieminski)