* Saudi crown prince to appear on "60 Minutes"
* Wall Street gains lift oil, supply worries weigh
* Coming up: Baker Hughes U.S. rig count data at 1 p.m. EDT (New throughout, updates prices, market activity, adds commentary)
NEW YORK, March 16 (Reuters) - Oil prices rose on Friday, on track for a weekly gain as market participants followed the U.S. stock market higher and looked to cover short bets ahead of a weekend in which the "60 Minutes" news program will air an interview with Saudi Arabia's crown prince.
Brent crude futures rose 76 cents to $65.88 a barrel, a 1.2 percent gain, by 12:16 p.m. EDT (1612 GMT). West Texas Intermediate (WTI) crude futures for April, which will expire on Tuesday, rose 94 cents to $62.13 a barrel, a 1.5 percent gain.
Earlier both contracts were up over a dollar.
Saudi Crown Prince "Mohammed bin Salman will be on '60 Minutes' on Sunday comparing Iran's Ayatollah to Hitler, and the battle in Ghouta, Syria, is ramping up," said John Kilduff, partner at investment manager Again Capital in New York. "You can't be short oil over the weekend with all that going on in the region."
Gains on Wall Street also supported prices as crude futures have recently been moving in tandem with U.S. stock indices.
Oil was on track for a weekly loss in early trade, but Friday's rise put them on course for a weekly gain.
On Thursday the International Energy Agency (IEA) said global oil demand is expected to pick up this year but supply is growing at a faster pace, leading to a rise in inventories in the first quarter of 2018.
The agency raised its forecast for oil demand this year to 99.3 million barrels per day (bpd) from 97.8 million bpd in 2017, and said it expected supply from non-OPEC nations to grow by 1.8 million bpd in 2018 to 59.9 million bpd, led by the United States.
OPEC and other producers have cut output to reduce a global crude glut. Investors will watch U.S. rig count data due at 1 p.m. EDT on Friday.
"Producers, as we've gone through earnings, are showing that they're going to remain disciplined even with a little more supportive oil price, which we think is healthy for the market," said Matt Sallee, a portfolio manager at Tortoise Capital in Leawood, Kansas.
Sallee added that he expected the data to show a small pickup in rig counts.
On Wednesday, the U.S. government reported that crude stockpiles in the United States increased by a more-than-expected 5 million barrels.
Political risk linked to Tehran increased after Rex Tillerson was sacked as U.S. secretary of state in favor of an Iran and North Korea hawk. Saudi Arabia's crown prince said Riyadh would develop nuclear weapons if Iran did so.
(Additional reporting by Scott DiSavino in New York and Julia Payne in London; Editing by David Gregorio)