The rest of the huge slick from the sunken tanker is about one kilometre off the north-west shore. Strong winds are expected to force it ashore soon.
A small French research submarine arrived in Spain on Sunday.
It will be used as soon as the weather permits to investigate whether fuel is still leaking from the sunken ship.
Local residents held a demonstration in the regional capital Santiago di Compostela on Sunday, as anger grew over the management of the crisis.
Trade unions and opposition parties supported the march, calling for Galicia to be declared a disaster area.
The protesters accused the authorities of not responding to the oil spill in an effective manner, and they called for the resignations of those accountable.
The province has spent the past two weeks cleaning up its previously pristine coast after an initial 6,000-ton slick came ashore, wrecking the local economy which depends largely on fishing.
The 26-year-old, single-hulled Prestige was damaged in a heavy storm and sank on 19 November while being towed out to sea.
New leaks feared
The first patches of oil from the second major slick arrived north of Cape Finisterre on Sunday morning.
With atrocious weather conditions hampering any attempts to prevent the fuel washing ashore, the rest of the slick is expected to hit the coast within hours.
"What's left for us to do except pick up our suitcases and leave? It's all over," said fisherman Manuel Boullosa.
"We face ruin," said Ramon Diaz. "Finisterre has no factories or anything - nothing but what comes from the sea."
This slick is believed to have leaked out when the Prestige broke in two and sank.
But new patches of oil have also been sighted above the spot where she went down, provoking fears that her remaining cargo of oil could be escaping.
Previously, it had been suggested the oil would solidify on the seabed, preventing any new pollution.
Local anger
The previous slick fouled more than 100 beaches and forced a fishing ban along 400 km of coastline.
The BBC's Claire Marshall said the spill was having a devastating effect on the region's economy, especially in the run-up to Christmas when seafood is popular.
Meanwhile, the Spanish Green Party has asked the country's chief prosecutor to assign criminal responsibility for the disaster.
The Greens say the government is at fault for tugging the tanker out to sea rather than bringing the Prestige to port where the oil could have been unloaded.
The government says it was motivated by fears that the tanker would break up nearer the shore causing worse damage.