* No deal after Trump, Schumer meet
* 10-year Treasury yields highest since Sep 2014
* Euro zone stock index hits 10-yr high (Updates with U.S. market close, oil settlement prices)
NEW YORK, Jan 19 (Reuters) - World equity markets climbed to a record on Friday as the U.S. dollar held near three-year lows and a U.S. government shutdown loomed, while U.S. Treasury yields continued their ascent to hit their highest levels since September 2014.
Democratic Senate leader Chuck Schumer met with President Donald Trump at the White House to search for ways to avert a U.S. government shutdown, but Schumer said afterward that disagreements remained as the clock ticked toward a midnight deadline to pass a funding bill.
Legislation to stave off an imminent federal government shutdown encountered obstacles in the Senate on Thursday night, despite the passage of a month-long funding bill by the House of Representatives hours earlier.
Without an infusion of new money, no matter how temporary, hundreds of thousands of "non-essential" federal workers may be put on furlough, while "essential" employees, dealing with public safety and national security, would continue working.
"Whatever immediate concern the government shutdown brings to the market, I think it will swiftly overcome," said Mark Luschini, chief investment strategist at Janney Montgomery Scott in Philadelphia.
Equity markets have historically shrugged off government shutdowns.
Shares on Wall Street rose modestly, with each of the major Wall Street indexes marking their third straight weekly gain.
The Dow Jones Industrial Average rose 53.91 points, or 0.21 percent, to 26,071.72, the S&P 500 gained 12.27 points, or 0.44 percent, to 2,810.3 and the Nasdaq Composite added 40.33 points, or 0.55 percent, to 7,336.38.
For the week, the Dow rose 1.04 percent, the S&P 500 advanced 0.86 percent and the Nasdaq rose 1.04 percent.
The trade-weighted dollar index was last up 0.1 percent, but was on pace for its fifth straight weekly drop, and is down nearly 2 percent so far in 2018. The euro was down 0.14 percent to $1.222.
European shares closed higher as confidence grew about corporate earnings and the strength of the global economy. The euro zone's STOXX benchmark index closed up 0.73 percent at 402.95 points, its highest level in 10 years and the pan-regional STOXX 600 benchmark rose 0.5 percent to 400.71 points, a 2-1/2 year peak.
The pan-European FTSEurofirst 300 index rose 0.49 percent, also a 2-1/2 year high, and MSCI's gauge of stocks across the globe gained 0.46 percent. MSCI's index notched its ninth straight week of gains.
Yields on the 10-year U.S. government note hit a three-year high as weakness in overnight trading led the debt to test key technical support levels, before the higher yields attracted new buyers.
The benchmark 10-year yield hit its highest level since September 2014 at 2.646 percent, breaking the 2017 high of 2.64 percent the market had been flirting with all week.
Benchmark 10-year notes last fell 12/32 in price to yield 2.6555 percent, from 2.611 percent late on Thursday.
Oil prices retreated and snapped a four-week streak of gains, as a bounce-back in U.S. production outweighed ongoing declines in crude inventories.
U.S. crude settled down 0.9 percent at $63.37 per barrel and Brent was last at $68.61, down 1 percent on the day.
(Additional reporting by April Joyner; Editing by Nick Zieminski)