* Wall Street trades higher, European shares gain
* Euro broadly higher after ECB's Draghi comments
* Oil rebounds on tensions between Syria and Turkey
By Wanfeng Zhou
NEW YORK, Oct 4 (Reuters) - The euro jumped against the dollar on Thursday while global shares edged higher on encouraging comments from European Central Bank President Mario Draghi and data showing a smaller-than-expected rise in U.S. jobless claims.
Oil prices rebounded after a steep fall in the previous session as escalating tensions between Syria and Turkey raised concerns over supplies from the Middle East.
Draghi, speaking after the ECB's decision to keep rates at 0.75 percent, said the bank is ready to buy the bonds of troubled euro zone economies that ask for it, leaving the door open to a widely expected bailout of Spain. He said the decision has eased tensions in the region's debt crisis.
"Draghi is infusing confidence into the markets today," said Art Hogan, managing director of Lazard Capital Markets in New York.
"We get reassured that we have the structure to figure this out," Hogan said about mechanisms to ease the crisis.
The euro rose 0.5 percent to $1.2972. Against the yen, it gained 0.7 percent to 101.95 yen.
U.S. stocks opened higher. The Dow Jones industrial average gained 35.59 points, or 0.26 percent, to 13,530.20. The Standard & Poor's 500 Index gained 4.52 points, or 0.31 percent, to 1,455.51. The Nasdaq Composite Index dropped 1.48 points, or 0.05 percent, to 3,133.75.
The number of Americans filing new claims for unemployment benefits rose less than expected last week, according to the latest weekly data, adding to modest signs of improvement.
The all-important government nonfarm payrolls report will be released on Friday.
The MSCI global stock index edged up 0.4 percent to 334.49. Europe's FTSEurofirst 300 index was slightly down at 1,100.12.
Brent crude rose $1.31 to $109.48 per barrel, after falling to its lowest since Sept. 20 on Wednesday. U.S. crude rose 73 cents to $88.87, after dropping to its lowest since Aug. 3 in the previous session.
Turkey's military hit targets inside Syria for the second day on Thursday after a mortar bomb fired from Syrian territory killed five Turkish civilians, marking the most serious cross-border escalation of the 18-month-old uprising in Syria.
"The hostilities between Syria and Turkey reinforce supply fears, as a number of pipelines cross the region," said Carsten Fritsch, oil analyst at Commerzbank in Frankfurt.
The benchmark 10-year U.S. Treasury note was down 7/32, with the yield at 1.6387 percent.