Deputy Prime Minister Mariano Rajoy said a change in wind direction was now pushing the slicks from the Galician shore southwards and out into the Atlantic.
Mr Rajoy said a French mini-submarine sent down to examine the wreckage had detected four small streams of solidified oil emerging from the tanker's bow and floating towards the surface, but he insisted there were no major leaks.
Neighbours Portugal and France are on high alert for oil approaching their coastlines, while the Spanish Government's handling of the crisis is coming under increasing criticism.
The single hull of the ageing tanker cracked during fierce storms last month, spilling between 10,000 and 20,000 metric tons of its 77,000-ton cargo off the Galician coast.
It then broke apart while being towed further out to sea on 19 November.
The two parts now languish on the sea bed some 250 kilometres (155 miles) west of Spain.
Experts hope the fuel oil will have solidified due to the low temperatures.
Local anger
Dozens of beaches along the Galician coastline have already been contaminated by thick sludge, and the local fishing industry has been thrown into crisis.
Thousands of people have been working frantically for days to try to keep the slicks at bay, using their own nets, shovels and trawlers to try to scoop oil away from the region's vital shellfish beds.
Opposition parties and environmental groups have accused the government in Madrid of not reacting quickly enough to the disaster.
"We could all have done better, not just the government," Mr Rajoy said.
Portuguese emergency workers have been setting up booms to try to protect key fisheries and nature reserves from the oil, although officials have expressed confidence that the country will escape widespread pollution.
France is also taking measures to protect its coastline, and is sending more surveillance planes to monitor the progress of the slicks.