LONDON  - Oil prices edged higher in rangebound trade on Monday on optimism over a rebound in the U.S. economy as coronavirus vaccinations accelerate, though rising COVID-19 cases in other parts of the world kept a lid on prices.

Brent was up 29 cents, or 0.5%, at $63.24 a barrel by 1006 GMT. West Texas Intermediate (WTI) U.S. crude rose 17 cents, or 0.3%, to $59.49.

The prices have remained rangebound in the past three weeks, with Brent between $60 and $65 a barrel and WTI at $57 to $62.

"Oil prices are entering a consolidation phase after swinging wildly last month," said oil broker PVM's Stephen Brennock.

"While there are still plenty of reasons to be bullish, market players have become more cautious as infections have surged in Europe, India and some emerging markets, while vaccine rollouts have proved slower than anticipated."

India now accounts for one in every six daily infections worldwide, with cases also rising in other parts of Asia. 

Asian oil demand remained weak and some buyers have asked for lower volumes in May, partly because of refinery maintenance and higher prices.

The United States has fully vaccinated more than 70 million people but U.S. gasoline demand has not picked up as much as expected.

The U.S. economy is at an "inflection point" amid expectations that growth and hiring will accelerate in the months ahead, but it faces the risk of reopening too quickly and sparking a resurgence in coronavirus cases, Federal Reserve Chair Jerome Powell said in an interview broadcast on Sunday.

"There really are risks out there. And the principal one just is that we will reopen too quickly, people will too quickly return to their old practices and we'll see another spike in cases," Powell said in a CBS interview recorded on Wednesday.

Prices also found some support after Yemen's Iran-aligned Houthi movement said it had fired 17 drones and two ballistic missiles at Saudi targets, including towards Saudi Aramco refineries in Jubail and Jeddah. 

There was no immediate Saudi confirmation.

(Reporting by Bozorgmehr Sharafedin in Lonodn and Aaron Sheldrick in Tokyo Editing by Jason Neely and David Goodman ) ((bozorgmehr.sharafedin@thomsonreuters.com; Twitter: @bozorgmehr;))