Expectations of more Iranian crude flooding the oversupplied global market within months following a nuclear deal also continued to drag prices lower.
US benchmark West Texas Intermediate (WTI) for August delivery fell 20 cents to $49.95 and Brent crude for September dropped 14 cents to $56.51 a barrel in afternoon trade.
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The dollar got a boost after Federal Reserve chair Janet Yellen last week stuck to her forecast for an increase in the US central bank's key interest rate later this year, as the economy picks up pace.
A rise in interest rates will attract investors to the dollar because of the prospect of higher returns, driving up the currency's value.
Since oil is priced in dollars, a stronger US currency makes the commodity more expensive, denting demand and putting downward pressure on prices.
"Despite worries over Greece and the China stock sell-off, the Fed reiterated its intention to raise rates in 2015," Singapore's DBS Bank said in a market commentary.
"With Greece finally working with its creditors on a third bailout package, focus returned to monetary policy divergences," it said, referring to other countries planning to hold down interest rates.
Research house Capital Economics said "our expectation is that the dollar's strength will continue over the next year and a half, given the contrast in the prospects for monetary policy in the US and its major trading partners".
The return of Iranian oil "is adding bearish pressure as the market is trying to price in the crude expected to be introduced by the end of the year", said Ang of Phillip Futures.
Iran and six world powers last week agreed a deal curbing its nuclear programme that aims to prevent it building an atomic bomb.
In return the West will lift crippling economic sanctions and allow Iran to ramp up crude exports.
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