"A small number of customers are now sending oil and gas through the pipeline at low rates as part of a coordinated plan that allows Ineos to carefully control the flow and pressure in the system", the company said.
Brent crude, the benchmark internationally for oil prices, was down 19 cents early Monday sitting at $65.06 per barrel.
Ineos, operator of the Forties pipeline, said that the structure was being tested after repairs and that full flows should resume soon.
Currencies linked to commodity prices headed higher on Tuesday's price rally, with the Canadian dollar trading at $1.2675 after hitting a high of $1.2678, a level not seen since early December.
US West Texas Intermediate crude futures were at $59.73 a barrel at 4.21am GMT, down 24c from their last settlement.
"The confirmation that Forties is coming back...has the potential for capping Brent", said Olivier Jakob, analyst at Petromatrix.
Armed assailants blew up a pipeline pumping crude oil to the port of Es Sider on Tuesday, cutting Libya's output by up to 100,000 barrels per day (bpd), according to military and energy sources.
The North African country's output had been recovering in recent months after being held down for years amid armed conflict and unrest.
Mirotic scores 24 points off bench, Bulls beat Bucks
The Bucks already know that they can't afford to underestimate or play below their best against the Bulls. It was the second time the Bulls won at Milwaukee in 12 days, including a 115-109 victory on December 15.
Harry Kane set to start for Spurs as he chases new record
Meanwhile, Southampton are without the injured Cedric Soares and Ryan Bertrand as well as the suspended Charlie Austin. They have won just one of those games, a 4-1 victory against Carlisle in the 2010 Football League Trophy final.