(Fixes typo in first paragraph)
* U.S. employers add 156,000 jobs in August
* December Fed rate increase still seen as possible
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh
NEW YORK, Sept 1 (Reuters) - The U.S. dollar edged higher against a basket of major rivals on Friday after U.S. jobs data was seen as sufficiently strong to support the possibility of another interest rate increase from the Federal Reserve this year.
Traders initally sold the dollar in a knee-jerk reaction to Labor Department data showing nonfarm payrolls increased by 156,000 last month, below expectations of economists polled by Reuters for a gain of 180,000.
A one-tenth of a percentage point uptick in the unemployment rate to 4.4 percent and tepid wage growth also briefly sent the dollar lower.
The dollar reversed its losses and pushed higher, however, with the euro last down 0.3 percent at $1.1870 after briefly hitting a session high of $1.1979. The dollar index, which measures the greenback against a basket of six major currencies, was last up 0.2 percent at 92.822 after initially plunging 0.5 percent.
"This is not out of line with the Feds thinking on the economy," said Thierry Albert Wizman, global interest rates and currencies strategist at Macquarie Ltd in New York. If the markets are discounting a December (Fed rate hike) just on the back of this, its probably premature."
Wizman noted that manufacturing and construction payrolls were strong. Construction employment jumped by 28,000 last month, the largest gain since February.
The dollar also recovered since it was oversold heading into the employment report, said Alfonso Esparza, senior currency analyst at Oanda in Toronto. The dollar index rallied 0.7 percent on Wednesday in a partial rebound from its plummet late last week and on Monday after European Central Bank President Mario Draghi made no mention of the euro's strength at a gathering of central bankers.
That omission had been seen as a tacit green signal to euro bulls and led the euro to hit a more than 2-1/2-year high on Tuesday of $1.2069.
Traders' expectations for the August nonfarm payrolls data were also excessively high given strong ADP U.S. private payrolls data released earlier this week, said Oanda's Esparza.
"The (Fed) rate hike is still sort of a question mark, but (Friday's jobs data) wasnt that big a miss to take it totally off the table for the rest of the year," he said.
The dollar was last up 0.3 percent against the yen at 110.30 yen after slumping to a session low of 109.57 yen just after the jobs data.
(Reporting by Sam Forgione; Editing by Dan Grebler)