"Following my update yesterday, I'm delighted to be able to tell you that Charlie Rowley has made further progress overnight. He is no longer in a critical condition," Wilkinson said.
The director added that the progress in the Rowley's recovery gave cause for optimism.
The police have launched a murder investigation.
UK Defense Secretary Gavin Williamson accused Russia of carrying out the poisoning attack.
Moscow said that it regretted Sturgess' death and remained very concerned about the repeated poisoning incidents on British soil.
The Russian Embassy in the United Kingdom has said that Moscow would consider the Salisbury and Amesbury incidents as anti-Russia provocations by London if the UK side did not provide Russia with access to the investigation materials and the Skripals.