* 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 (New throughout, updates prices, market activity and comments)
NEW YORK, March 6 (Reuters) - Oil prices rose on Tuesday, supported by a weaker dollar but U.S. crude's gains were limited by forecasts for a weekly rise in U.S. crude stockpiles.
Brent crude futures rose 24 cents to $65.78 a barrel, a 0.4 percent gain, by 1:13 p.m. EST (1813 GMT).
U.S. West Texas Intermediate (WTI) crude futures edged up 3 cents, or 0.1 percent, to $62.60 a barrel.
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 dollar-denominated commodities cheaper for holders of other currencies.
"Initially, the market is looking at it as the positive side of this is the world will be doing business. It's one less risk on the table," said Phil Flynn, analyst at Price Futures Group in Chicago.
U.S. oil prices remained under pressure from expectations that weekly crude 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 official inventory data on Wednesday.
Inventories are rising ahead of the seasonal maintenance period for refineries, when shutdowns mean they need less crude.
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 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 was 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 helped lift Brent back above $65 a barrel this week. (Additional reporting by Amanda Cooper in London and Jane Chung in Seoul; Editing by David Gregorio)