* North Korea news hits dollar, supports oil prices
* Expected rise in U.S. crude inventories weighs
* OPEC, U.S. shale producers gather in Houston for CERAWeek
* Coming up: API U.S. crude inventory data (Updates prices, market activity, adds commentary; changes byline, dateline to NEW YORK, previously LONDON)
NEW YORK, March 6 (Reuters) - Oil prices were mixed on Tuesday, under pressure from forecasts for a weekly rise in U.S. crude stockpiles but supported by a weaker dollar.
Brent crude futures rose 6 cents to $65.60 a barrel, a 0.1 percent gain.
West Texas Intermediate (WTI) crude futures fell 17 cents to $62.40 a barrel, a 0.3 percent loss, by 11:45 a.m. EST (1645 GMT).
Oil drew support as the U.S. dollar fell to its lowest in more than a week against a basket of currencies on news from South Korea that North Korea was willing to hold talks with the United States on denuclearization, and would suspend nuclear tests during any discussions.
South Korea also said it would hold a summit with North Korea for the first time in more than a decade.
The news sent investors to sell the U.S. dollar and instead buy riskier assets such as commodities. A weaker dollar makes oil and other dollar-denominated commodities cheaper for holders of other currencies.
U.S. crude prices especially were under pressure from expectations that weekly inventory data would show a second straight rise, according to a Reuters poll. The American Petroleum Institute will release trade inventory data at 4:30 p.m. EST (2130 GMT) on Tuesday. The U.S. government issues its official inventory data on Wednesday.
Inventories are rising ahead of the seasonal maintenance period for refineries, when shutdowns mean they need less crude.
Rising U.S. output is also adding to stockpiles. U.S. crude production has risen to more than 10 million barrels per day (bpd), overtaking top exporter Saudi Arabia.
Output hit a record 10.057 million bpd in November, according to the U.S. Department of Energy.
"The rising oil-production profile in the U.S. remains the predominant bearish factor affecting prices," said Abhishek Kumar, senior energy analyst at Interfax Energy's Global Gas Analytics in London.
The continued growth of U.S. shale has also been a theme at the CERAWeek conference in Houston this week, said John Kilduff, partner at investment manager Again Capital in New York.
Brent had dipped closer to $65 in earlier trading, pressured by the International Energy Agency's (IEA) warning on Monday that U.S. oil output is set to surge over the coming five years.
The prospect of OPEC and other producers, including Russia, maintaining crude output cuts in the face of a boom in U.S. shale production has helped to push oil back above $65 a barrel this week. (Additional reporting by Amanda Cooper in London and Jane Chung in Seoul)