UPDATE 7-Oil prices slip from 3-yr highs but strong demand lends support

* OPEC/Russia-led supply restraint has propped up crude

* Goldman Sachs sees upside to its oil price forecast

* Morgan Stanley, BoAML raise crude price forecasts

* U.S. oil production has stalled due to icy weather

* But U.S. output expected to break through 10 mln bpd soon (Adds comments, India imports, updates prices, changes dateline, previous LONDON)

NEW YORK, Jan 16 (Reuters) - Oil prices eased from three-year highs on Tuesday as traders booked profits from the rally but healthy demand underpinned prices near $70, a level not seen since 2014's market slump.

Prices have been driven up by oil production curbs in OPEC nations and Russia, as well as strong demand thanks to healthy economic growth. Imports to India, the world's third-biggest oil consumer, rose by about 1.8 percent in 2017 to a record 4.37 million barrels per day (bpd) as the country boosted purchases to feed its expanded refining capacity.

Brent futures fell 74 cents, or 1 percent, to $69.52 a barrel by 10:55 a.m. EST (1555 GMT). Earlier in the day, the global benchmark lost more than $1 to a low of $69.16. Traders said Brent was well supported overall at around $70.

Brent hit $70.37 on Monday, matching a high from December 2014, when markets were at the beginning of a three-year decline.

U.S. West Texas Intermediate (WTI) crude futures were at $64.06 a barrel, down 24 cents, or 0.4 percent. WTI hit a December 2014 peak of $64.89 earlier in the session.

Most analysts and market participants said oil is vulnerable to profit taking as hedge funds and money mangers have amassed a record number of bullish bets on U.S. crude.

In addition, trading was thin on Monday due to a holiday in the United States.

Fundamentally, oil has been pushed higher by an effort led by the Organization of the Petroleum Exporting Countries and Russia to withhold production since January last year. The cuts are set to last through 2018.

Reacting to the recent three-year high, Russian Energy Minister Alexander Novak said the oil market was not yet balanced and that the global deal to cut output should continue as the price rise could be due to cold weather.

The restraint has coincided with healthy oil demand, pushing up crude by almost 15 percent since early December.

"This rally has been driven first by robust fundamentals, with strong demand growth and high OPEC compliance accelerating," U.S. bank Goldman Sachs said in a note.

"We see increasing upside risks to our $62 per barrel Brent and $57.5 per barrel WTI forecast for the coming months."

Other banks, including Bank of America Merrill Lynch, Societe Generale and Morgan Stanley, have upped their price forecasts.

"Our view is that prices are overheated, and will correct lower," SocGen said in a note. "We believe that the current situation, with strong uplift from fundamentals, non-fundamentals, and geopolitics all at the same time, is not sustainable."

A factor that held back crude prices in 2017, the surge in U.S. production, has stalled at least temporarily due to icy winter weather.

U.S. production <C-OUT-T-EIA> has fallen from 9.8 million barrels per day in December to 9.5 million bpd currently.

However, most analysts still expect U.S. production to break through 10 million bpd soon.

(Additional reporting by Julia Payne in London, Henning Gloystein; Editing by Dale Hudson and Marguerita Choy)