Police say a post-mortem on Peaches Geldof has proved inconclusive, and toxicology tests will be conducted in an attempt to determine cause of death.
The 25-year-old daughter of musician and campaigner Bob Geldof was found dead at her home in Kent on Monday.
Police said at the time that her death was being treated as "non-suspicious but unexplained and sudden".
The toxicology tests could take "several weeks" to come through, police said on Wednesday.
"Officers continue to investigate the circumstances surrounding the death in order to compile a report for the coroner," they added in a statement.
Kent County Council has said it will make "a decision on whether there needs to be an inquest" based on the final results of the post-mortem.
Geldof, who was a writer, TV presenter and model, died on Monday.
Officers had been called to the home she shared with her husband, singer Thomas Cohen, and their two young children following "a report of concern for the welfare of a woman". Geldof was pronounced dead at the scene.
The news of her death was met by shock and grief from friends and family.
In a statement issued on Monday night, Bob Geldof said: "She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.
"Writing 'was' destroys me afresh. What a beautiful child. How is this possible that we will not see her again? How is that bearable?"
Geldof's elder sister, Fifi Trixibelle, also paid tribute on Tuesday with a post on Instagram that read: "My beautiful baby sister.... Gone but never forgotten. I love you Peaches x."
Cohen, lead singer of the rock band SCUM, added: "My beloved wife Peaches was adored by myself and her two sons Astala and Phaedra.
"I shall bring them up with their mother in their hearts everyday. We shall love her forever."
Actress Susan Sarandon, singers Boy George and Lily Allen, and TV presenter Davina McCall all offered condolences.
Irish President Michael D Higgins extended "my deepest sympathies to Bob Geldof and his family on the sudden and untimely death of his daughter".
President Higgins, who was due to meet Bob Geldof this week during a state visit to the UK, said his thoughts were with the family.
"This is such a difficult cross to bear for any family and all of our thoughts are with Peaches' family and friends at this time. Sabina and I were due to meet Bob Geldof while on the state visit and we are thinking of him at this time of immense loss," he added.
Also among those to pay tribute was Michelle Mone, founder of underwear firm Ultimo, who employed Geldof as a brand ambassador.
She called her "an incredible young woman" and said their relationship remained good despite Geldof being dropped by the company in 2010 after allegations about her taking drugs appeared in newspapers.
"I really did respect her and every time I met her I just felt quite proud of her because she had managed to turn her life around and seemed very happy," Mone told BBC Radio 5 live.
Geldof was 11 when her own mother died.
TV presenter Paula Yates died of a drug overdose in September 2000. In September 2012 Geldof said she had not been able to come to terms with her mother's death for several years.
Geldof's final tweet on Sunday was a picture of her as a child in her mother's arms, with the message: "Me and my mum."
Her last column for Mother and Baby magazine was published posthumously on Tuesday.
"Right now, life is good," she wrote. "And being a mum is the best part of it."