* Euro, Sterling hold onto Monday's gains
* ECB debate shifting to rate path from quantitative easing, sources say
* Sterling rose as EU, Britain reached transition agreement
* Fed expected to signal faster increases in U.S. rates
SINGAPORE, March 20 (Reuters) - The euro on Tuesday held onto gains made the previous day when traders revived bets that the European Central Bank would raise interest rates sooner than previously thought.
The euro last changed hands at $1.2341, after gaining 0.4 percent on Monday.
The common currency had drawn strength on Monday from a source-based Reuters report that ECB policymakers are shifting their debate to how steeply interest rates should rise and how to phase out a bond buying programme after purchasing 2.5 trillion euros in over three years.
Sterling also stood tall after setting a one-month high against the dollar on Monday, as Britain and the European Union agreed to a 21-month post-Brexit transition period and a potential solution to avoid a "hard border" for Northern Ireland.
Sterling edged up 0.1 percent to $1.4035. On Monday, the pound had risen to as high as $1.4088, its strongest level since Feb. 16.
The strength in euro and sterling helped weigh on the dollar, which last stood at 89.870 against a basket of six major currencies, down from Monday's intraday high around 90.345.
Market participants are now pondering whether the U.S. Federal Reserve, which holds a two-day policy meeting that ends on Wednesday, will signal a faster pace of rate increases in the coming months as the labour market tightens further.
Interest rate futures imply traders have fully priced in a rate increase this week, which would raise the target range to between 1.50 percent and 1.75 percent.
Against the yen, the dollar held steady at 106.10 yen , staying above a 16-month low of 105.24 yen set in early March.
The dollar still appears heavy against the yen, with Japanese currency supported by signs of a retreat in investor risk appetite, said Stephen Innes, head of trading in Asia-Pacific for Oanda in Singapore.
"It's pretty easy to stay short dollar/yen in this environment given the risk aversion," Innes said.
The yen is a traditional safe haven currency that tends to attract demand in times of market turmoil.
U.S. equities fell on Monday, with the S&P and Nasdaq suffering their worst day in just over five weeks, as concerns over increased regulation for large tech companies was spearheaded by a plunge in Facebook shares. (Reporting by Masayuki Kitano; Editing by Simon Cameron-Moore)