The body of Alice, 14, was found in the River Brent in west London on 30 September after she went missing a month earlier.
The corpse of Latvian builder Zalkalns was found less than two miles away in Boston Manor Park, on 4 October.
The Met Police has told the Crown Prosecution Service it thinks Zalkalns was responsible for Alice's murder.
At a briefing, the force released the evidence it had compiled against him, including CCTV and items recovered.
Alice's disappearance sparked what the Met said was its largest inquiry since the 7/7 bombings in 2005.
A statement from her family said they had "serious unanswered questions" about "what the authorities knew or should have known" about Zalkalns "when he came to the UK".
"Alice believed in the free movement of people and so do we," the statement added. "For her sake we are determined to ask these questions responsibly and sensitively."
At the briefing, Det Ch Insp Andy Chalmers said: "Boy, do I wish we'd found her earlier."
Zalkalns, who was working as a labourer on a building site in Isleworth, had been convicted of murdering his wife in Latvia in 1998.
Police said they believe there was a "sexual motive" to Alice's murder although there is no evidence of that.
The CPS said its case would have been based on circumstantial evidence, not forensic or eyewitness evidence.
Tim Thompson, CPS prosecutor said: "Of all the people the various strands of evidence might have implicated they in fact point towards Arnis Zalkalns: a person who has previously killed and concealed the body of a young woman.
"It is not for the CPS to say whether or not Arnis Zalkalns killed Alice Gross - that would have been for a jury to decide."
They added a single DNA sample from Alice's skin "strongly supports" a match to Zalkalns.
Officers have said no-one else was involved in Zalkalns' death. He was found hanged.
Post mortem tests suggested the cause of of Alice's death was "compressive asphyxia".
Following the police briefing, Alice's family said: "Although we now have certain information about how Alice died, we are still left with some serious unanswered questions about what the authorities knew or should have known about the man who is believed to have killed our daughter when he came to the UK."
The inquest into Alice's death was due to resume on Thursday but has been postponed.
Other key points that have emerged from police at a press briefing:
Scotland Yard also spoke about Zalkalns' criminal history.
Following his conviction for murdering his wife in Latvia, he was released from prison in 2005 and arrived legally in the UK in 2007, police said.
In 2009, he was arrested over an alleged indecent assault on 14-year-old girl near to the Grand Union Canal in Boston Manor.
Police said the allegation was "thoroughly investigated" but the complainant decided not to press charges.
No checks were made to see if Zalkalns had any overseas convictions because it was not Met policy to do so, the force said.
However, detectives said even if the conviction had been known about it was "very unlikely" Zalkalns would have been deported.
Emma Norton, legal officer for civil rights group Liberty, which is representing Alice's family at her forthcoming inquest, said: "Liberty has made representations to the coroner that the inquest into Alice's death must be an Article 2 inquest - that is, an inquest that will look not only into the cause of her death, but also into the wider circumstances.
"In particular, the family wants to know what the authorities knew or ought to have known about Zalkalns when he travelled to the UK from Latvia.
"The family is aware that this is a sensitive and difficult subject, and is concerned to ensure that it is not hijacked by groups with an anti-immigration agenda."
Charges would have been brought against Alice Gross murder suspect Arnis Zalkalns if he had lived, police say.