FOREX-Dollar up for third day, eyes on Fed and Greece

* Euro falls to three-week low of $1.1062

* Dollar/yen hits highest since March 20

* Sterling helped by BoE (Shenzhen: 000725.SZ - news) minutes

* Eyes on Fed, ECB meeting on Greece

* Fed minutes looked to after stronger U.S. housing numbers (Updates prices, adds more comment)

By Patrick Graham

LONDON, May 20 (Reuters) - The dollar touched a three-week high against the euro before halting on Wednesday, a third day of gains adding to a growing sense the U.S. currency may be ready for another run higher after its weakest period in four years.

Another push below $1.10 per euro in the short term should depend largely on upcoming economic data, and Federal Reserve minutes later on Wednesday will provide more fodder for the argument over whether the U.S. central bank can raise interest rates this year.

The dollar topped out at a three-week high of $1.1062 in early European deals and was trading at $1.1117 by mid-morning, still up a third of a percent on the day.

Sterling resisted the charge, gaining 0.3 percent to $1.5558 on the back of some new signs of unease over ultra-low rates and the housing market from the Bank of England.

"Things have shifted in the last few days and I would be short euros even from here," said a senior currency dealer with one international bank in London.

"The ECB clearly does not want the euro to go to $1.15 and the dynamic is moving back onto the dollar."

Some analysts pointed to headlines over Greece as weakening the euro, but most said the biggest element was the sense that the past month's 8 percent pullback has cleaned out many long-term bets on the dollar, leaving room for new action.

"Positions are a lot cleaner and that may well have opened the way to another push higher," said Josh O'Byrne, a strategist with Citi in London.

"If this is the beginning of a dollar resurgence, then the Canadian dollar, Norwegian crown and rouble are interesting bets on the downside."

The yen fell by around a quarter of a percent weaker to 120.95 yen per dollar. The dollar was half a percent higher against the Norwegian crown and more than 1 percent higher against the rouble.

A raft of major banks have forecast the dollar to push past parity with the euro over the next year and had cast the past month's weakness as a correction after the greenback topped out at almost $1.04 per euro in March.

Any encouragement from the Fed minutes for the view the bank could still tighten this year might give the dollar another push. A discussion at the European Central Bank on Wednesday of whether to trim the life-support it is providing cash-strapped Greek banks also holds risks for the euro.

"Our economists think today's minutes will ... be consistent with their view that the Fed seems poised to begin tightening in September," said Adam Cole, Head (Other OTC: HEDYY - news) of G10 FX Strategy at RBC (Other OTC: RBCI - news) in London.

"Despite the small back-up in US yields this week, markets still only discount the first Fed hike around January 2016, so such a message should add to dollar gains." (Additional reporting by John Geddie; Editing by Hugh Lawson and Toby Chopra)