* U.S. factory orders raise worry over weaker economy
* Dollar strengthens, weighing on crude futures
* U.S. sanctions on Venezuela further tighten supply
* Coming up: API U.S. oil inventories data at 4:30 p.m. EST (21:30 GMT) (Updates prices, adds analyst comments, market details)
NEW YORK, Feb 5 (Reuters) - Oil prices fell on Tuesday, pulling back from two-month highs as concerns over a global economic slowdown crept back into the market and a stronger dollar also weighed.
Prices sagged a day after the release of weak U.S. factory order data, which, coupled with recent disappointing economic data out of China, stoked worries about softer demand for crude oil in 2019, analysts said.
Brent crude futures fell 39 cents to $62.12 a barrel. They touched their highest level in more than two months at $63.63 the previous day. U.S. crude futures dropped 82 cents to $53.74 a barrel, down 1.5 percent, at 2:03 p.m. EST (1903 GMT).
Oil also felt pressure from a strengthening dollar, which rallied for a fourth straight session, which makes crude more expensive for non-U.S. buyers, said Phillip Streible, senior commodities strategist at RJO Futures.
Meanwhile, investors shifted assets into equities and away from markets more sensitive to Washington-Beijing trade relations and movements in the dollar, Streible said.
"Oil is just not in favor today, and they are going after the equity markets," he said. Wall Street was slightly higher on Tuesday.
U.S. sanctions on Venezuela were viewed as supportive of prices by helping to tighten global supplies. Numerous tankers are currently in the water off the Venezuelan coast, unable to move because state-owned PDVSA is demanding payment, which would run afoul of U.S. sanctions.
Supplies of heavy crude oil like that produced in Venezuela are scarce, as other providers including Mexico and Canada have also faced challenges to output and export.
The Organization of the Petroleum Exporting Countries and its allies, including Russia, agreed to production cuts effective from last month to beat back supply growth.
A Reuters survey found that supply from OPEC states had fallen the most in two years, with Saudi Arabia and its Gulf Arab allies over-delivering on pledged cuts while Iran, Libya and Venezuela registered involuntary declines.
Concerns about the pace of global economic growth remained. New orders for U.S.-made goods fell unexpectedly in November, with sharp declines in demand for machinery and electrical equipment, according to data released on Monday.
The global economic outlook and prospects for growth in fuel demand have also been clouded by poor economic data in China and U.S.-China trade tensions. (Reporting by Laila Kearney in New York Additional reporting by Noah Browning and Ron Bousso in London and Colin Packham in Sydney Editing by Susan Thomas and Matthew Lewis)