A 21-year-old woman was found with two stab wounds to the chest at a unit in Kingswood, in Sydney's west about 1.40pm, after another person at the unit called emergency services, NSW Police Detective Superintendent Trent King told reporters on Monday.
Police alleged a man in a domestic relationship with the woman had caused her injuries.
"He is now wanted in relation to her death," Det Supt King said.
The 22-year-old was last seen running from the unit complex wearing a black jacket, black pants and a red and black basketball singlet.
"We do know who he is," Det Supt King said.
"We are very keen to speak to this person, we want to do it as soon as possible."
Police had not previously been called to the address and there were no court orders to protect either person, he said.
The man being sought by police had a non-violent history involving minor transport infringements.
"However, nothing relating to violence and nothing related to domestics," Det Supt King said.
Police believe it was a targeted attack with no ongoing threat to the public, but warned against approaching the man.
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