Janbaz Tarin, 21, is wanted after Raneem Oudeh, 22, and Khaola Saleem, 49, were stabbed in Solihull on Monday as Ms Oudeh was on the phone to police.
Ms Oudeh was Mr Tarin’s ex-partner and had made a number of calls to police on the day of her death.
West Midlands Police said a £5,000 reward was being offered for information leading to his arrest.
Detectives believe Mr Tarin is still in the West Midlands area and that people are protecting him.
Det Insp Caroline Corfield said: “Someone out there knows where he is. Janbaz Tarin deserves no protection.”
In a video released by the force, Det Supt Mark Payne appealed directly to the suspect.
“So if Mr Tarin is watching this, hand yourself in. We will find you,” he said.
A post-mortem examination on Tuesday found Miss Oudeh and her mother, who were born in Syria, died from multiple stab wounds.
Miss Oudeh, who has a two-year-old son, had been on the phone to police in the early hours of Monday when “the situation quickly escalated,” police said.
“The call handler immediately dispatched officers to the location in Northdown Road where they arrived within minutes,” police said on Tuesday.
The two women were found in the street outside their home shortly after 00:30 BST and were confirmed dead at the scene.
Mr Tarin – an Afghan national who arrived in the UK on Christmas Day in 2012 – was previously in a relationship with Miss Oudeh but is not the father of her son.
Police said several addresses in Birmingham linked to Mr Tarin had been searched, and computer equipment and mobile phones seized for examination.
The suspected murder weapon has also been recovered and a van seized for forensic examination.
West Midlands Police has referred itself to the Independent Office for Police Conduct as it had previous contact with the victims’ family.