* Brent, US oil head for biggest weekly climb since April
* US jobless data buoys prices
* But Brent faces headwinds from increased Libyan output
SINGAPORE May 16 (Reuters) - Brent futures held above $109 a barrel on Friday as fresh tensions over Ukraine kept them on course for their biggest weekly rise since mid-April, but returning Libyan supply capped gains.
U.S. crude futures were also heading for their best week in five, bolstered by data indicating the U.S. economy could be firming.
U.S. Secretary of State John Kerry warned Russia it faced broader economic and industrial sanctions from the United States and Europe if it meddled in Ukraine's presidential elections on May 25.
"The situation with Ukraine is stopping (oil) sellers being too aggressive," said Ric Spooner, chief market analyst at CMC Markets in Sydney.
Price differentials between Brent contracts for June and July also helped push prices higher, said Ken Hasegawa, commodity sales manager at Newedge Japan.
"Brent is trying to fill the gap between the June contract, which expired on Thursday and the new contract for July," Hasegawa said.
Brent crude for July delivery had risen 25 cents to $109.34 a barrel by 0320 GMT, up from $109.09 after the new front contract took effect on Friday.
Expiring Brent crude for June rose 25 cents to settle at $110.44 a barrel on Thursday.
U.S. crude for June delivery climbed 47 cents to $101.96 a barrel on Friday, after falling 87 cents to settle at $101.50. The June contract expires on Tuesday.
"Fewer U.S. jobless claims offset weaker production data and tempered any weakness in the economy," said Spooner.
U.S. unemployment claims dropped to a seasonally adjusted 297,000 last week - the lowest since May 2007.
But gains in U.S. crude prices could be tempered following the release of housing starts figures at 1230 GMT, which Spooner said might miss forecasts.
Total U.S. crude inventories climbed to 398.5 million barrels in the week to May 9, although stocks at the key Cushing, Oklahoma delivery hub fell by 592,000 barrels, government data showed.
Brent could also face headwinds from the gradual resumption of output from Libya, where the El Feel oilfield has returned to full capacity and the Wafa field is operating after being blocked by protesters.
Libya's oil output is 300,000 barrels per day (bpd) after the two fields came back on line, the National Oil Corporation (NOC) said.
Investors are also keeping an eye on talks due to end Friday over Tehran's nuclear program.
Iran could be curbing its crude exports within limits agreed in November by Tehran and the six powers as part of the interim pact which partially eased sanctions over the nuclear program.
Iran's oil exports averaged 1.11 million barrels per day (bpd) in April, the second month in a row exports have fallen, the Paris-based International Energy Agency said. That is close to the 1 million bpd allowed under November's pact.
(Reporting by Keith Wallis; Editing by Joseph Radford)