Police increased their resources from 20 to 24 staff working on the inquiry today.
They say there may have been a sexual element to the attack, and evidence indicates the victim was killed by someone she knew or was familiar with.
Mr Rae said there was a "sense of urgency'' as many people the team needed to talk to would soon be going away for holidays over the Christmas break.
The number of 24 officers did not include members of the force's specialist search team, who have been searching gardens, rubbish bins, culverts and house roofs for an unspecified item.
Mr Rae expected the specialist search team would continue searching throughout today. He could not elaborate further as to what the team was searching for, except to say there was one item in particular which may be missing from the house and may be related to the attack and it had still not been found.
If the search team's efforts continued to prove unsuccessful police may seek the public's help in looking for the item.
Police were still looking for information from the public. If anybody had seen people or a person around the house or in the general vicinity of the Cass Street house in the early hours of Saturday morning, or had heard someone talking about being there, or knew of someone who had unexplained injuries or unexplained blood stains on their clothing, they should contact police.
Mr Rae said police were no closer to finding out whether a bloody hand print found on a clothing bin near the house was related to the attack, and this would most likely have to be determined forensically.
Sina was attacked after her sister's partner dropped her home between 2.20am to 2.30am on Saturday, after finishing a CMP Canterbury shift at 1am and going to a friend's place. She suffered injuries from an unidentified blunt object and a sharp blade, including cuts to her face and throat.
She was discovered fatally injured by her step brother at about 2.36am. It is unknown whether Sina's attacker came to the door after she entered the house alone, or was already in the house.
Mr Rae said it was unknown whether the attacker had intimate knowledge of Sina's movements and knew she would be home alone at the time.
"She wouldn't usually be home by herself,'' he said.
Sina lived at the house with seven other family members including her three-year-old daughter, but all were at another family property in town at the time.
Tributes have continued to flow on a Rest In Paradise Sina Solomona page set up on Facebook, with one contributor yesterday saying people would not rest until justice had been done.
