Officers said murder suspect Habibur Masum, 25, remained at large but a 23-year-old man had been arrested on suspicion of assisting an offender.
Speaking at a press conference on Monday, Assistant Chief Constable Damien Miller said Ms Akter died after being stabbed "multiple times".
"I believe Masum is still in the country at this moment in time," ACC Miller added after confirming airports and ports had been warned to be on the lookout for him.
Det Supt Jude Holmes from GMP Oldham district said: "We share the shock and concern that our communities feel in the wake of this tragic incident, and our thoughts are with Kulsuma Akter's family at this truly distressing time."
He is described as a slim Asian man and was last seen wearing a duffle coat with three large horizontal lines, grey tracksuit bottoms and maroon trainers.
Clarification 8 April 2024: An initial incorrect spelling of Kulsuma Akter supplied by West Yorkshire Police was updated to accurately reflect her name.
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