Police say they believe the Clapham chemical attack suspect is being "helped by others" and are "targeting more of his associates".
In an update on Tuesday afternoon, police released an image of the 35-year-old's last known sighting at 10.04pm last Wednesday, when he passed the Unilever building in central London - on the north bank of the River Thames - and headed towards Victoria Embankment.
Commander Jon Savell said teams have been "working tirelessly through the night and into today" to pinpoint Ezedi's latest movements.
"It remains our belief that he is being helped by others and yesterday we arrested a man for assisting an offender," he said, referring to a 22-year-old detained on Monday.
"Our enquiries continue to target more of Ezedi's associates."
A £20,000 reward is on offer for information leading to Ezedi's arrest, with police revealing the substance used in the attack was "very strong", "concentrated" and "corrosive".
The woman, who was known to Ezedi, remains in hospital in a critical but stable condition and may lose sight in her right eye, police said on Monday.
Meanwhile, her daughters - aged eight and three - have injuries not thought to be life-changing.
Ezedi allegedly threw the younger child to the ground during the attack at 7.25pm before attempting to drive away from the scene, crashing into a parked vehicle and fleeing on foot.
The manhunt, led by the Met's Specialist Crime Command, involves a team of more than 100 officers and dozens more from forces across the UK, including in Northumbria, and British Transport Police.
Police said "painstaking work" by counter terrorism officers - drafted in to examine hundreds of hours of CCTV - traced Ezedi from his last-known position at 9.47pm on Allhallows Lane in the City of London.
At 9.54pm he travelled along Upper Thames Street and into Pauls Walk, passing the City of London School and then towards Blackfriars Bridge.
That brought him to his most recent sighting at 10.04pm, six days ago.
More than 200 calls have been received about potential sightings, but they have since been discounted.
It is understood Ezedi, who is believed to be from Afghanistan, arrived in the UK in 2016, reportedly in the back of a lorry.
According to the PA news agency, he avoided jail after pleading guilty to charges of sexual assault and exposure.
Instead, he was placed on the sex offenders register for 10 years and told to do 200 hours of unpaid work when he was handed a suspended sentence at Newcastle Crown Court on 9 January 2018.
The details emerged as a bishop said she would make no apologies for religious leaders supporting asylum seekers.
Questions remain around how Ezedi was granted asylum despite his conviction, amid suggestions a tribunal judge ruled in his favour after a priest confirmed he had converted to Christianity.