* Iran supply concern boosts prices
* Obama says "no silver bullet" for high gasoline prices
* Brent close to record high in euros (Previous SINGAPORE, updates prices)
LONDON, Feb 24 (Reuters) - Oil rose towards $124 a barrel on Friday, heading for a fifth straight weekly gain, as concern over cuts in Iranian supply offset worries that high oil prices could restrain demand.
European buyers of Iranian oil have cut back on purchases ahead of an EU embargo on Iran's oil imports effective July 1. Some of Iran's biggest customers in Asia including China have also reduced purchases.
Brent crude rose 16 cents to $123.78 by 0904 GMT, after trading as high as $124.28 earlier. It reached $124.50 on Thursday, the highest intra-day price since May 3. U.S. crude was up 48 cents to $108.31, extending its rally into a seventh day.
"The supportive factors are on the supply side - Iran and Iran and Iran, with a bit of Syria and Sudan," said Christopher Bellew, a broker at Jefferies Bache in London. "It would not be at these numbers if it was not for the supply-side problems."
Japan, the world's third-largest oil importer, may cut Iranian crude imports by a more-than-expected 20 percent as it seeks a waiver from U.S. sanctions. Last year, the country bought almost 9 percent of its crude from Iran.
Iran said on Thursday it had maintained oil production levels despite sanctions, but analysts said they suspected Tehran was storing crude at sea while looking for new customers to evade Western measures.
Supply concerns over Iran, as well as production losses in Syria and South Sudan, have offset concern about economic problems in Europe and a weaker global demand outlook.
In euros, the price of Brent reached a record high on Thursday, adding rising fuel costs to the euro zone's debt troubles.
Greece's second bailout since 2010 was sealed by euro zone finance ministers on Tuesday, averting the threat of a chaotic default next month but doing little to allay doubts about the country's long-term financial stability.
Oil demand in Europe is falling and consumption in the United States -- the world's top consumer -- has hit the lowest level in nearly 15 years, a report from the Energy Information Administration showed this week.
Even so, upbeat U.S. economic data on Thursday pointed to a more robust picture for demand. The number of Americans filing new claims for jobless benefits held at a four-year low, while December home prices rose 0.7 percent.
President Barack Obama said on Thursday there was no "silver bullet" for high gasoline prices. Lawmakers from his own party are asking him to take steps to ease the price pressure in the short term.
Democratic lawmakers on Wednesday urged the White House to signal it is ready to tap the country's strategic petroleum reserve. Obama made no mention of taking that step in his speech. (Reporting by Alex Lawler and Florence Tan in Singapore; Editing by Alison Birrane)