* Dollar down after Bullard, Mester comments

* Last week’s dovish Fed statement still hitting dollar

* Draghi speech, Greece in focus in Europe

By Ahmed Aboulenein

LONDON, March 23 (Reuters) – The euro rose on Monday, reversing early losses to build on its best weekly performance since late 2011 versus the dollar, which came under pressure after comments by U.S. Federal Reserve officials.

St Louis Fed President James Bullard told CNBC on Monday that the dollar index was not far from fair value and it was unclear how much more the currency would strengthen against the euro.

Analysts said the comments reflected some unease among policymakers at the dollar’s strength, echoing remarks last week by Fed Chair Janet Yellen.

The euro was up 0.6 percent at $ 1.08950 while the dollar index shed 0.5 percent to 97.440.

“The clear outcome from the FOMC meeting was that it was seen as dovish,” said John Hardy, currency strategist at Saxo Bank in Copenhagen, adding that Bullard’s comments weighed on the dollar.

“It feels like the market does want to consolidate a bit here, this $ 1.075-1.08 area has been a sticking point but I think we will get to $ 1.10-1.11 pretty quickly and if that falls then we’re talking $ 1.15 all of a sudden.”

Also on Monday, Cleveland Fed President Loretta Mester said U.S. monetary policy easing had created only minimal bubble-like activity in financial markets.

Bets in favour of the dollar fell to a three-month low in the past week, according to data from the Commodity Futures Trading Commission released on Friday. Net dollar longs fell below $ 40 billion for the first time in 12 weeks.

Speculators cut long positions in the dollar last week after markets pushed back expectations of when U.S. rates would rise, and Yellen said the Fed noted that export growth has weakened, with the strong dollar probably one reason for that.

Morgan Stanley said in a note that the dollar was likely to remain soft especially if incoming data surprised on the downside. “We recommend selling dollar/yen with a target of 115.50 and a stop at 121.20 yen,” they said.

Dollar/yen was down 0.2 percent at 119.75 yen on Monday.

The euro fell earlier in the day over concerns about whether Greece can reach agreement with creditors to secure fresh funds.

European Central Bank President Mario Draghi was due to address a European Parliament committee, with Greece and the progress of the ECB’s quantitative easing programme, which has pushed the euro lower recently, high on the agenda.

A Berlin meeting between Greek Prime Minister Alexis Tsipras and German Chancellor Angela Merkel was also in focus.

(editing by John Stonestreet)