GLOBAL MARKETS-Greek pledge and cautious Fed soothe investors

* Euro set for best week in over two years

* U.S. stocks set to open higher on weakening dollar

* Brent set to rack up third weekly price drop

* Greek yields fall after Athens' assurances (Updates prices, adds U.S. stocks)

By John Geddie

LONDON, March 20 (Reuters) - The euro headed for its best week in more than two years on Friday while yields on low-rated bonds fell as investors welcomed the Fed's caution on rate hikes and a reform pledge from Athens that could avert a cash crunch.

Illustrating the problems low inflation is causing for central banks looking to normalise monetary policy in countries such as the United States and Britain, oil was set to rack up its third consecutive weekly price slump.

Futures showed Wall Street set to open 0.3 percent higher, with stocks on course for their best week in a month, as a Fed-induced weakening of the dollar gave a boost to U.S. exporters.

European shares edged up while euro zone bond yields fell after assurances from Athens that it will submit reforms needed to unlock bailout cash. The ECB's trillion euro asset purchase scheme was also in focus at the end of its second week.

"The outlook for European markets is better than it has been for years, and the risks now are largely political," said Christian Schultz, senior economist at Berenberg.

Greek bond yields dropped 45 basis points to 12.10 percent, while Portuguese, Spanish and Italian equivalents were all down around 1-2 bps. German bonds -- the euro zone benchmark -- were flat at 0.19 percent, just above a record low.

The euro was 0.5 percent higher against the dollar at $1.0712, well below Wednesday's high above $1.10 but leaving the single currency on track for its best week since January 2013.

"What's been dominating the euro over the course of the last week has been the moves in the dollar. The FOMC announcement was, on margin, more dovish than expected," said Phyllis Papadavid, senior global FX strategist at BNP Paribas (Xetra: 887771 - news) in London.

The pan-European FTSEurofirst 300 share index was up 0.3 percent at 1.601.42 points, having hit a new 7-1/2 year high just after markets opened.

The impetus gained from Wednesday's dovish statement from the U.S. Federal Reserve has begun to ease, but European indices were supported by gains in the construction sector after Holcim and Lafarge (Paris: FR0000120537 - news) agreed to new merger terms.

Asian stocks were broadly unchanged, with MSCI (NYSE: MSCI - news) 's broadest index of Asia-Pacific shares outside Japan up 0.05 percent after rallying 1.3 percent the previous day. It was on course for a gain of over 2 percent for the week.

The region's decliners included shares in Hong Kong, Malaysia, South Korea and Thailand. Australian and Chinese stocks were among the gainers in a choppy session.

The dollar index was down 0.5 percent at 98.72 but still well above a low of 96.628 plumbed midweek. The index was on track for slight loss on the week after touching a 12-year high above 100.00 on March 13.

The dollar saw its biggest fall in six years against the euro on Wednesday, after the Fed's dovish statement.

In commodities, Brent crude oil was down 1.3 percent at $53.69 a barrel, hurt by oversupply worries after Kuwait said OPEC had no choice but to maintain output levels.

U.S. crude was down around 0.5 percent, just above the six-year low of $42.03 a barrel hit earlier in the week. (Editing by Catherine Evans)