* Brent notches biggest weekly gain since 2009

* U.S. crude has biggest weekly rise since 2011

* Focus shifts to implementation and impact of OPEC deal

* Russia's output hits new post-Soviet high ahead of cut

* Data shows U.S. drillers added 3 oil rigs in week to Dec. 2 (Updates to settlement)

By Devika Krishna Kumar

NEW YORK, Dec 2 (Reuters) - Oil prices rallied for their best week in at least five years on Friday, steadying above $51 a barrel, following OPEC's decision to cut crude output to rein in a global glut that has weighed on prices for more than two years.

After the deal was announced on Wednesday, the market focused on the implementation and impact of OPEC's first output cuts since 2008, to be joined by Russia and possibly other non-OPEC producers.

Crude prices were pressured by data showing oil output in Russia rose in November to a post-Soviet high and Moscow's plan to use its record November oil production as its baseline when it cuts output.

With cuts being implemented next year only against end-2016 levels, analysts said there was still a possibility that oversupply, which has halved oil prices since 2014, remains a factor next year.

"Global, and especially U.S., crude oil inventories are currently at extremely high levels after two years of massive oversupply," Societe Generale analysts said.

"While the OPEC agreement is very significant and will result in some moderate global stockdraws next year, it is likely to take more than one year for crude inventory levels to return to more normal levels."

Front-month Brent crude futures ended the session up at $54.46 a barrel, up 52 cents, 0.96 percent. The contract rose more than 15 percent for the week, its biggest gain since early 2009.

U.S. crude settled at $51.68 per barrel, up 62 cents or 1.21 percent and notched its biggest weekly gain since early 2011, with a rise of 12 percent.

Oil drew support from a weak dollar, which slipped against a basket of currencies. Still, traders said profit-taking ahead of the weekend limited crude's price gains.

"The petroleum markets have settled into quieter mixed flows as the waves created by Wednesday's OPEC announcement gradually dissipate, with some light profit taking emerging in crude oil," said Tim Evans, energy futures specialist at Citigroup.

"A weaker U.S. dollar is typically supportive for commodity prices and may have helped steady crude oil from the lows in today's trade."

Prices rose to session highs after the White House said it expects U.S. President Barack Obama to sign U.S. legislation extending sanctions against Iran for 10 years into law.

Iran is also seen as a wild card in the execution of the OPEC deal.

U.S. President-elect Donald Trump's transition team is examining proposals for new non-nuclear sanctions on Iran, the Financial Times reported on Friday.

Iran had threatened on Friday to retaliate against the U.S. Senate's vote to extend the Iran Sanctions Act (ISA) for 10 years, saying it violated last year's deal with six major powers that curbed its nuclear program.

The sanctions were first adopted in 1996 to punish investments in Iran's energy industry and deter its pursuit of nuclear weapons.

Meanwhile, U.S. energy companies extended their recovery in oil drilling into a seventh month this week, data from energy services firm Baker Hughes Inc showed on Friday.

(Additional reporting by Ron Bousso in London, Henning Gloystein and Roslan Khasawneh in Singapore; Editing by Andrew Hay and Chizu Nomiyama)