The suspect in the Clapham alkali attack was in a relationship with the injured woman, police believe, and the breakdown of that relationship may have been the motive.
Abdul Shokoor Ezedi, 35, is believed to have arranged a meeting with the woman, who is still sedated in hospital.
In its latest update, police said he is wanted for attempted murder.
He was last seen on 31 January, after an attack on a mother and her two girls with corrosive liquid in south London.
The Metropolitan Police called on Ezedi to hand himself in.
Police said there is a “very strong indication” that Ezedi had been in a relationship with the woman but it had broken down.
He arranged to meet the woman before attacking her with the chemical, police said.
The woman and her two children travelled to the agreed meeting spot in a car and were then assaulted in that same vehicle, police say.
They said it is believed all four of were together in the car when the attack took place.
“We can’t give any details about how long the relationship had taken place or how it broke down,” Cdr Jon Savell told a press briefing.
The 31-year-old woman remains sedated and in hospital. Police say she may lose sight in her right eye as a result of the attack.
The Met released a new last known location for Ezedi hours after the attack.
CCTV shows him crossing Vauxhall Bridge and onto Vauxhall Bridge Road at 23:00 GMT on Wednesday.
Police said that Ezedi’s injuries appear “very significant” and could even be fatal if not treated. They do not believe he has received hospital treatment.
There are many theories about where the suspect could have escaped to, police said.
“He could have gone north, he could have gone east, south, west or he could have gone abroad,” Cdr Jon Savell said.
He added there is a possibility Ezedi could have gone into the River Thames, but there have been no reports of anyone entering the river and no bodies have been recovered that match his.
At the police briefing, Darius Nasimi, of the charity Afghanistan and Central Asian Association, said his organisation was working closely with the police to make sure the Afghan community are reached as widely as possible.
“Violence against women and girls cannot be tolerated,” he said, before issuing a plea for anyone harbouring Ezedi or helping him to avoid capture to come forward.
Police believe Ezedi, who is from the Newcastle area but believed to have travelled to the UK on a lorry from Afghanistan in 2016, is not the father of the children, aged eight and three, injured in the attack and was in the capital visiting their mother.
Ezedi travelled to London from Newcastle in the early hours of Wednesday before the attack happened outside a Clapham hotel in Lessar Avenue at 19:25.
The mother and two girls were hurt after the substance was thrown at them.
Ezedi then attempted to drive away from the scene, crashing into a stationary vehicle and fleeing on foot.
Five Met Police officers were also injured as they responded to the attack, as were four members of the public who tried to help.
