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* Dollar inches up but set for fourth straight weekly fall
* Yen pushed lower as Bank of Japan buys bonds
* U.S. payrolls expected to be show robust growth of 175,000
* Graphic: World FX rates in 2016 tmsnrt.rs/2egbfVh
By Marc Jones
LONDON, Feb 3 (Reuters) - The dollar inched fractionally higher on Friday and limped towards U.S. jobs data facing its fourth straight weekly fall, adding to what has already been its worst start to a year in three decades.
The U.S. currency has been hit hard by worries about both Donald Trump's presidential style and a lack of clarity from the Federal Reserve this week about when it is likely to next raise interest rates.
The non-farm payrolls report due at 1330 GMT is expected to show employers added 175,000 jobs in January, figures that if achieved are likely to be robust enough to give markets confidence in bets on a hike at least by June.
The dollar index, which tracks the greenback versus six top currencies, was up 0.3 percent and back above 100 having gained most of its the early traction against the yen after the Bank of Japan made a surprise move to push down its bond yields.
Having muscled its way up to 113.15 yen, the greenback then caught a tailwind in Europe that lifted it against the euro, the pound and the Swiss franc, although it couldn't quite overcome a Norwegian crown which has now risen six weeks running.
It also made little difference to what was set to be the dollar index's first unbroken run of four weekly falls in two years, that has driven it down almost 3 percent since the start of the year. The dollar fell 2.6 percent in January - its worst showing since 1987.
"Markets are now really seeing the downside of Trump, especially the immigration orders," said Rabobank U.S.-focused economist Philip Marey.
He added the upcoming non-farm payrolls data should reassure the Fed especially if broader employment and wage rates rise. "But it is also important they know which way the fiscal winds are blowing and of course they don't at the moment.
One of the main beneficiaries of the dollar's wobble has been the euro.
It was set for its sixth week of gains in at $1.0741 and having gone as high as $1.0829 after the latest signs growth and inflation is rising in the euro zone. That has a read-across for the European Central Bank's stimulus programme.
Britain's sterling was licking its wounds after a bruising few days that have brought this year's mini-rally to a halt.
Having suffered its worst day since October on Thursday, it was knocked again as data on the UK's dominant services sector fell for its first time in four months. It squeezed the pound below $1.25 and to 86 pence per euro and was on course for near 1 percent weekly drop.
"It was surely too early for markets to expect a significantly more hawkish narrative," from the Bank of England which on Thursday signalled little urgency to raise UK interest rates, analysts from Bank of America Merrill Lynch said.
"A benign interpretation of the Brexit process and strong UK data had perhaps lulled the sterling market into a false sense of near-term security."
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Reporting by Marc Jones; Editing by Tom Heneghan