* U.S. crude short-covering after rally on inventory rise
* U.S. implements tariffs on Chinese goods on Friday
* Saudi Arabia raises oil supply sharply in June
* South Korea stops loading Iran oil as U.S. sanctions loom
* Baker Hughes rig count shows increase of 100 y-o-y (Adds comment, Baker Hughes data; updates prices)
NEW YORK, July 6 (Reuters) - Oil was mixed on Friday, with short-covering pushing up U.S. crude futures while Brent slipped on global trade tensions and increased Saudi production.
West Texas Intermediate crude futures gained 80 cents to $73.74 by 1:48 p.m. (1748 GMT). Global benchmark Brent was down 29 cents at $77.10 a barrel.
For the week, WTI was on track for a loss of about 0.5 percent after hitting a 3-1/2-year high on Tuesday. Brent was on track for about a 3 percent loss.
"When we moved into June, WTI was $12 under Brent," said Walter Zimmerman, chief technical analyst at ICAP-TA.
"So when you get this wave of fear with Libya, Canada, Iran, and Venezuela, a fear that maybe things are going to get tight, people buy what's cheap; they buy what's undervalued - and that was WTI."
Friday's rally was also due to investors short-covering after WTI fell almost 2 percent on Thursday, said Bob Yawger of director of energy futures at Mizuho in New York.
U.S. crude was pressured on Thursday by data showing an unexpected 1.3 million-barrel build in inventories.
The U.S. rig count, an early indicator of future output, was up by five in the week to July 6, according to General Electric Co's Baker Hughes energy services firm.
That brings the total count to 863, up 100 from last year.
Brent, meanwhile, was "still having difficulty gaining independent bullish traction," said Jim Ritterbusch, president of Ritterbusch and Associates in a note.
"Increased Saudi crude availability that is being enhanced by reduced OSPs (official selling prices) into Europe and other regions is providing a strong counter against curtailed Libyan export activities," Ritterbusch wrote.
In addition to reducing the price of its August barrels, Saudi Arabia told the Organization of the Petroleum Exporting Countries that it increased production by almost 500,000 barrels per day last month.
OPEC and its allies have trimmed production since January 2017, but agreed this month to boost output in part due to involuntary supply drops in Venezuela, Angola and Libya.
Imminent shifts to global oil trade flows were also influencing prices.
China has indicated that it could place tariffs on U.S. oil. If that happens "Chinese demand would then shift to other suppliers. Because the oil market is already in tight supply due to the numerous outages, this would drive international prices (Brent) further up," Commerzbank said in a note.
Renewed U.S. sanctions on Iranian oil may further tighten supplies.
South Korea, a major buyer of Iranian oil, will not lift any Iranian crude in July for the first time since August 2012, three sources familiar with the matter said.
(Additional reporting by Alex Lawler in LONDON, Henning Gloystein in SINGAPORE and Meng Meng in BEIJING Editing by Susan Thomas, Marguerita Choy and Jan Harvey)