* 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 to settle, adds commentary)
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 25 cents to settle at $65.79 a barrel, a 0.4 percent gain. Brent reached a low of $65.30 a barrel and a six-day high of $66.16 a barrel during the session.
West Texas Intermediate (WTI) crude futures rose 3 cents to settle at $62.60 a barrel. WTI notched its own six-day high at $63.28 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 led investors to sell the U.S. dollar and instead buy riskier assets such as commodities.
The dollar index last was down by half a percent. 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.
Analysts polled by Reuters ahead of the data on average expect U.S. crude stocks rose by 2.7 million barrels in the week ended March 2.
While overall stocks have risen, inventories at the Cushing, Oklahoma, storage hub have declined for 10 consecutive weeks.
"Any larger-than-expected upswing in total stocks could easily be negated by another sharp decline in Cushing supplies that could drive renewed support into the WTI curve," Jim Ritterbusch, president of Chicago-based energy advisory firm Ritterbusch & Associates, said in a report.
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 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.
April U.S. gasoline futures rose as much as 0.50 percent to hit $1.9443 a gallon, the highest since Jan. 30, before retreating. (Additional reporting by Amanda Cooper in London and Jane Chung in Seoul; Editing by David Gregorio and Andrea Ricci)