* Iran, U.S. signal will to engage as new president Rouhani takes oath
* U.S. hiring slows in July but jobless rate falls to 4-yr low
* Renewed protests keep Libya oil exports below half of normal
* Coming Up: U.S. ISM Non-manufacturing PMI; 1400 GMT
By Manash Goswami
SINGAPORE, Aug 5 (Reuters) - Brent oil rose above $109 a barrel on Monday after promising China data, but prices may struggle to hold on to gains as risk premiums come off after Iran and the United States signalled a fresh will to end the dispute over Tehran's nuclear programme.
Newly elected Iranian President Hassan Rouhani, who was sworn in on Sunday, called for dialogue to reduce "antagonism and aggression". Within hours the United States followed, saying it was ready to work with Rouhani's government if it were serious about engagement.
Brent crude gained 5 cents to $109 a barrel by 0257 GMT, after touching as low as $108.30 and hitting an intraday high of $109.13. U.S. oil fell 2 cents to $106.92, after slipping to as low as $106.01.
"Given the change of tone in Iran and comments from the United States, we are seeing risk premiums surrounding the Middle East and Iran coming off," said Jonathan Barratt, chief executive of Sydney-based commodity research firm Barratt's Bulletin. "It is a good change, and will weigh on prices."
The United States and Europe have slapped tough sanctions on Iran, pushing the country's oil exports down by more than half, to force it to halt its nuclear programme. Tehran has retaliated with threats to block a key route that ships most of the oil exported from the Middle East.
Worries about supply amid the simmering tensions have kept oil above $100 a barrel for most of 2012 and this year even though a weak global economy has reduced demand growth.
But a weaker-than-expected jobs report from the United States, the world's biggest economy and top oil consumer, may cap oil price gains. The number of jobs outside the farming sector rose by 162,000 last month, the smallest gain in four months and below analysts' expectations.
"We are also seeing some adjustments in prices after Friday's jobs report," Barratt said.
Brent is expected to drop into a range of $106.76-$107.40, while U.S. oil is expected to drop into a range of $104.12-$105.02, Reuters technical analyst Wang Tao says.
China's services sector expanded, defying the broad cooldown, as new business orders recovered from a multi-year low in a rare sign of resilience.
While positive data from the world's No.2 oil consumer cushioned prices, crude also got support from worries about supply from key exporters such as Libya and Iraq and smaller supplier Yemen.
Libya's oil exports were flowing at less than half of normal rates on Friday as strikes and protests kept major terminals shut in one of the worst disruptions to hit the North African OPEC producer in the past year.
Shipments from Iraq may be cut by between 400,000 and 500,000 barrels per day in September. Tribesmen blew up Yemen's main oil export pipeline late on Saturday, halting the flow of crude. (Editing by Himani Sarkar)