UPDATE 7-Oil eases on expected U.S. crude inventory build, stronger dollar

* Dollar hits one-week high

* Wall Street rally supports oil prices

* Coming Up: U.S. Federal Reserve minutes

* U.S. crude stocks forecast rising for fourth week - poll

* Coming Up: API data on U.S. oil inventories at 4:30 p.m. (Updates market prices, adds commentary; changes byline, dateline, previous LONDON)

NEW YORK, Feb 21 (Reuters) - Oil prices softened on Wednesday ahead of data expected to show rising crude inventories in the United States and as the dollar strengthened from last week's three-year lows.

Brent crude futures for April delivery were little changed, falling 1 cent to $65.24 a barrel by 12:37 p.m. EST (1727 GMT).

West Texas Intermediate crude (WTI) futures for April delivery, the new front month, fell 18 cents, or 0.3 percent, to $61.61 a barrel.

Traders are awaiting the latest data on U.S. inventories from the American Petroleum Institute, set to be released at 4:30 p.m. EST (2130 GMT) and government figures due on Thursday at 11 a.m., both delayed a day due to a holiday on Monday.

U.S. crude stocks likely rose 1.3 million barrels in the week ended Feb. 16, the fourth consecutive weekly build, according to a preliminary Reuters poll.

U.S. crude oil production surpassed 10 million barrels per day (bpd) in November for the first time since 1970, hindering efforts by the Organization of the Petroleum Exporting Countries and other producers, led by Russia, to reduce bloated global inventories and prop up oil prices by cutting output.

Also bearish for oil, the dollar strengthened against other major currencies, buoyed by a rise in short-term U.S. government bond yields to a nine-year high.

Oil gained some support by a gain on Wall Street.

"Oil prices and the S&P have been highly correlated, of late, with economic strength translating into improved company performance and higher energy demand," said John Kilduff, partner at investment manager Again Capital in New York.

Investors will be watching the release of minutes from the Federal Reserve's most recent policy-setting meeting, which may signal the pace of any interest rate rises. Worries about increasing inflation have rattled markets in recent weeks.

Futures prices have also been dented by physical crude markets, which are showing signs of seasonal weakness as refineries prepare to shutdown for maintenance between peak summer and winter fuel demand periods.

(Additional reporting by Amanda Cooper in London and Henning Gloystein in Singapore Editing by Marguerita Choy)