* Sterling falls vs dollar on UK economy worries
* Euro tumbles vs Swiss franc to 17-month low (Updates prices)

By Steven C. Johnson

NEW YORK, March 19 (Reuters) - The euro fell on Friday over doubts Greece would win euro-zone aid, capping its worst week since January, and concerns about the UK economy hit sterling.

A report on Thursday that Greece saw limited prospects for euro-zone assistance raised concerns about the country's ability to service its debt. On Friday, the euro fell as far as $1.3502, its lowest level in more than two weeks. It was down 1.7 percent this week, its worst showing since late January.

Greece said it may have to turn to the International Monetary Fund for help, though it dismissed news reports it was planning to do so as early as April.

If Greece fails to win euro-zone support, analysts say the market may view the euro zone as unwilling or unable to solve internal financial crises.

The tensions surrounding Greece are escalating. This whole IMF situation has become a game of brinkmanship and the whole uncertainty is undermining the euro, said Michael Woolfolk, senior currency strategist, at BNY Mellon in New York.

European Union leaders are set to meet next week to discuss rescue plans for Greece. The euro was last trading at 1,3535, down about half a percent, while investors demanded a higher premium to buy 10-year Greek debt over German bunds.

Sterling also fell sharply, dipping briefly below $1.50 GBP, after a Bank of England policy maker said there was some risk of a double-dip recession in Britain. The pound was last down about 1.5 percent at $1.5017.

European Central Bank President Jean-Claude Trichet and other officials have ruled out IMF assistance to Greece, but German policy makers have said the IMF may have a role to play.

From the perspective of the investor, events continue to be frustratingly opaque, said Andrew Wilkinson, senior market analyst at Interactive Brokers Group in Greenwich, Connecticut. Repeated meetings result in no clear statement other than a commitment that now appears far less solid than before.

A decline in major U.S. stock indexes on Friday reflects heightened risk aversion, BNY Mellon's Woolfolk said, and could spell more trouble for the euro.

I really don't see any support for the euro. We may have to test that low below $1.3450 in the near term, he said.

YEN FLAT, SWISS FRANC RISES

The dollar was up 0.2 percent at 90.47 yen while the euro fell 0.4 percent to 1.4346 Swiss francs.

Earlier, the euro slipped as far as 1.4320 francs, a 17-month low, following Thursday's remarks from a Swiss National Bank official. Board member Jean-Pierre Danthine said interest rates cannot stay low forever and Swiss firms and consumers should prepare for higher borrowing costs.

But at a policy meeting last week, the SNB's statement did not drop a pledge to counter excessive gains in the franc as it continues to appreciate against the euro.

Traders are focusing on the 1.4300 area, the record low, as the next support level. Options structures were said to be prevalent at that level.

The Canadian dollar gained after Canadian core inflation unexpectedly rose in February. Earlier, the U.S. dollar fell to a 20-month low at C$1.0062, but the greenback recovered to trade up 0.2 percent at C$1.0166. (Additional reporting by Gertrude Chavez-Dreyfuss; editing by Andrew Hay)

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