Brent crude futures settled at $60.90 a barrel, up 46 cents. Brent has gained 9.5 percent in the last 16 trading days.

U.S. West Texas Intermediate (WTI) crude futures settled up 25 cents at $54.15 a barrel, highest since Feb. 23, 2017. The U.S. contract has been strong of late as well, gaining 10 percent in the last 16 trading days.

"The market has now held over $49/bbl for over a month, establishing that as the low end of the new range," wrote analysts at Drillinginfo.com.

The Organization of the Petroleum Exporting Countries plus Russia and nine other producers agreed to cut 1.8 million barrels per day from January 2016 to clear a supply glut.

The pact, already renewed once, runs to March 2018. But Saudi Arabia and Russia, which are leading the effort, have voiced support for a further extension.

OPEC Secretary General Mohammad Barkindo said Russian-Saudi backing for an extension cleared the fog before the group's meeting in Vienna on Nov. 30.

Saudi Crown Prince Mohammad bin Salman over the weekend repeated the kingdom's support for extending the deal.

"The market has rallied pretty significantly and I think it's predicated on the fact that the Saudis and Russians are continuing the cut agreement," said Gene McGillian, manager of research at Tradition Energy in Stamford, Conn.

Monday's rally pushed Brent's December 2017 contract to a premium of $2.60 a barrel over the December 2018 contract .

This structure, known as backwardation, was at the top of OPEC's "to do" list, along with targeting record-high global inventories. Such a premium gives holders of physical oil an incentive to sell their stored barrels for a higher price, thus tightening markets.

"A lot of the investment firms are raising their price targets so there’s a bit of a change in sentiment," said John Kilduff, partner at Again Capital LLC in New York.

J.P. Morgan raised its 2018 Brent and WTI forecasts by $11 and $11.40 to $58 and $54.63 per barrel, respectively. The bank said the revision reflects OPEC and non-OPEC cuts and higher- than-expected demand growth tightening the oil market.

However, traders said a 900,000 bpd export capacity increase from Iraq's southern ports, to 4.6 million bpd, had prevented Brent rising further.

Iraq has increased exports from its southern oilfields to 3.45 million bpd to make up for a shortfall from the northern Kirkuk fields, Basra Oil Company Director General Ihsan Abdul Jabbar said.

(Additional reporting by Ahmad Ghaddar in London, Henning Gloystein in Singapore; Editing by Chizu Nomiyama and Dan Grebler)

By Julia Simon