UPDATE 2-Oil rises after 2-day fall, gains limited by stronger dollar

* Data shows larger-than-expected build in U.S. crude stocks

Gasoline stockpiles rise unexpectedly

* Soaring U.S. output offsets OPEC's higher compliance with cuts (Adds detail, updates prices)

By Osamu Tsukimori

TOKYO, March 1 (Reuters) - Oil prices edged up on Thursday after sharp falls in the previous two sessions, though gains were limited as some investors shied away from riskier assets amid volatile equity markets and a stronger dollar.

Both global benchmark oil futures fell sharply on Wednesday after government data showed a larger-than-expected rise in U.S. crude inventories.

U.S. West Texas Intermediate crude for April delivery was up 13 cents, or 0.2 percent, at $61.77 a barrel by 0741 GMT. It settled the previous session down 2.2 percent.

Brent crude for May delivery, the new front-month contract, was up 17 cents, or 0.3 percent, at $64.90. The April contract expired on Wednesday, down 1.3 percent.

Both benchmark contracts fell nearly 5 percent in February, the first monthly declines in six months.

"An extended large decline in equities has been prompting investors to avoid risk assets such as oil," said Tomomichi Akuta, senior economist at Mitsubishi UFJ Research and Consulting in Tokyo.

Some industry sources said Wednesday's drop was also due to profit-taking by market participants at the end of the month after oil hit a three-week high earlier this week.

Meanwhile, oil has been under pressure as the dollar index rose to a five-week high.

U.S. crude inventories rose by 3 million barrels last week, compared with analyst expectations for a build of 2.1 million barrels, weekly data by the Energy Information Administration (EIA) showed.

Gasoline stocks also rose by 2.5 million barrels against expectations for a 190,000-barrel drop.

Soaring U.S. crude output has also kept a lid on oil prices this year, even though producers, led by the Organization of the Petroleum Exporting Countries and Russia, have reduced output.

U.S. crude oil production rose to a record 10.057 million barrels per day (bpd) in November and retreated slightly in December to 9.949 million bpd, the EIA said on Wednesday.

"Despite the expanding output curbs by OPEC and non-OPEC members such as Russia, the market has been focusing more on rising U.S. output since around late January," Akuta added.

OPEC, meanwhile, is doing its part to counter U.S. output. The group's oil production fell in February to a 10-month low, a Reuters survey found on Wednesday.

Oil prices may find some support as the U.S. is considering oil-related sanctions on OPEC member Venezuela to pressure its socialist President Nicolas Maduro, a U.S. official said on Wednesday.

(Reporting by Osamu Tsukimori Editing by Joseph Radford and Christian Schmollinger)