NEW YORK, Oct 23 (Reuters) - Oil fell roughly $1 a barrel on Friday and headed for a weekly drop on rising Libyan crude supply and demand concerns caused by surging coronavirus cases in the United States and Europe. Crude prices sank after Libya's National Oil Corp (NOC) said it lifted force majeure on exports from key ports and output would reach 1 million barrels per day in four weeks.

"As soon as that came out, the market cratered," said Bob Yawger, director of energy futures at Mizuho in New York. Brent crude lost 93 cents, or 2.2%, at $41.53 a barrel by 1:21 p.m. EDT (1721 GMT). US crude shed $1.01 cents, or 2.5%, at $39.63. Both contracts are on track for a weekly loss.

Italy and several US states reported record daily increases in infections, while France extended curfews for about two thirds of its population as the second wave of the Covid-19 pandemic sweeps across Europe, raising fears about fuel consumption.

"What's holding us back is the uncertainty about demand - when we're going to get a vaccine, when things are going to get back to normal, concerns about more shutdowns," said Phil Flynn, senior analyst at Price Futures Group in Chicago.

Comments by Russian President Vladimir Putin on Thursday that Moscow did not rule out extending OPEC+ oil output cuts, but did not go far enough to support prices against the weight of Libyan output and demand fears, analysts said.

OPEC+, a group that includes Russia and the Organization of the Petroleum Exporting Countries, is due to increase production by 2 million bpd in January 2021 as part of a plan to pump more as demand recovers.

However, the second wave of the pandemic and resulting slowdown in the demand recovery have raised the question of whether the increase is premature. Adding to supply pressures, the US energy companies added five oil rigs to 287, its highest since May, energy services firm Baker Hughes Co said. The rig count is an indicator of future supply.