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UPDATE 6-Oil prices soften as Libyan output undermines 2018 rally

* Restarting Libyan oilfields put brake on rally

* Saudi comments, global growth offer some support

* U.S. drillers cut rigs in week to Jan. 19 (Updates prices)

LONDON, Jan 22 (Reuters) - Oil slipped on Monday under pressure from rising Libyan output and concerns that a rally that had sent prices to their highest since December 2014 had run out of steam.

But losses were limited by comments from top exporter Saudi Arabia that OPEC and other producers would continue to cooperate on oil output cuts beyond 2018. Prices also found some support from strong economic growth that underpinned demand.

Brent crude slipped 12 cents to $68.49 a barrel by 1454 GMT, reversing after modest gains earlier in the day. Brent on Jan. 15 had hit $70.37, the highest since December 2014.

U.S. crude fell 14 cents to $63.23, having also hit its highest since December 2014 last week.

PVM analyst Tamas Varga said the resumption of output from Libya's As-Sarah fields was "serving as a brake on the rally".

"The downside might be limited but last week's highs are unlikely to be penetrated unless there is a significant bullish change on the supply front," he said in a report.

Production at As-Sarah resumed on Sunday and was expected to add 55,000 barrels per day by Monday.

Brent is particularly sensitive to changes in output from Libya, as most Libyan crude is priced against Brent.

Saudi Arabia said on Sunday the Organization of the Petroleum Exporting Countries and its allies had agreed to continue cooperating on production after their deal on supply cuts expires at the end of 2018. The deal began in January 2017.

Saudi Energy Minister Khalid al-Falih said market rebalancing might not occur until 2019, suggesting it would take longer than OPEC had previously indicated.

Bernstein Energy said oil inventories might start rising soon due to a slowdown in demand that typically happens at the end of the northern hemisphere winter.

But a drop in the number of U.S. drilling rigs, an indicator of future output, offered some support. U.S. drillers cut five rigs in the week to Jan. 19, reducing the count to 747.

Global economic growth was also helping prices by driving up demand. "Global growth has become synchronised and accelerated above trend," U.S. bank Morgan Stanley said in a note.

(Additional reporting Ahmad Ghaddar in London and Henning Gloystein in Singapore; Editing by Dale Hudson and Edmund Blair)