Officials said that while there were no visible signs of fire on the Stena Immaculate, there were still small pockets of fire on the top deck of the Solong. Firefighting vessels were continuing to provide support.
Chief coastguard Paddy O'Callaghan said the Solong had now been towed "to a safe location", while the Stena Immaculate remained anchored in its original position.
Three aerial surveillance flights had taken place on Wednesday and found no indication of pollution on the surface of the water attributable to either of the vessels, he added.
The Marine Accident Investigation Branch (MAIB) said it was leading the safety investigation into the incident, with Portugal and the US acting as "substantially interested states".
A spokesperson for MAIB said the investigation was focused at present on gathering witness accounts and obtaining digital data.
A detailed inspection of both vessels, along with the retrieval of data recorders, would be carried out when it was safe to do.
Following the collision, the Russian national captain of the Solong was arrested on suspicion of gross negligence manslaughter following reports of a missing crew member.
Ernst Russ said it was working on plans to recover the vessel and was assisting the authorities with their investigations.
The company said its thoughts remained with the family of the missing crew member.
Humberside Police said it had begun a criminal investigation into the cause of the collision and was working with the Maritime and Coastguard Agency.
"Detectives are continuing to conduct extensive lines of enquiry alongside partners in connection with the collision," the force said.