The contentious hearing, which led to swarms of media, yielded few developments.
The brothers' attorney Mark Geragos declared he would seek the recusal of the Los Angeles County District Attorney's Office from the case and prosecutors asked the court to review a new report about whether the brothers could be a danger to the public if released.
The judge is set to consider those requests at the May hearing date.
The resentencing bid is one of three paths the brothers' attorneys have been chasing to potentially secure a future release.
Thursday's developments muddled the timeline for any potential decision on the brothers' fate.
The hearing on Thursday was supposed to centre on one subject: Should the Menendez brothers be resentenced to a lesser penalty.
The day was set to include testimony from witnesses involved in the case and members of their family. There was even the possibility of the brothers taking the stand and pleading their case.
Mr Geragos has also asked Judge Michael Jesic of the Superior Court of Los Angeles to reduce their conviction to manslaughter, which could pave the way to a faster release.
Judge Jesic will ultimately make the determination about whether to issue a new sentence or reject their request. He could also issue a different sentence that would make them eligible for parole.
Several members of the Menendez family who support their release had travelled to Los Angeles to testify.
The brothers themselves appeared in court via a video feed from a San Diego prison, wearing identical cobalt blue prison uniforms.
But the hearing was derailed by a development in another bid they've been chasing for freedom: Clemency from California Gov Gavin Newsom.
Newsom had ordered the state's parole board to examine the case, and that panel completed a risk assessment report this week. The report examines whether the brothers would be a risk to society if released.
Prosecutors said in court filings that they want to review the report before moving ahead with the resentencing effort.
Mr Geragos argued that he, too, had not been able to view the report yet.
Late in the afternoon, Judge Michael Jesic agreed to pause the proceedings until 9 May to give the court and attorneys time to review the risk assessment.
That hearing will consider what parts of the report, if any, will be admissible during the resentencing hearing.
The court will also consider a motion Mr Geragos intends to file to recuse the district attorney's office from the case.
Mr Geragos and a lawyer representing the Menendez family members, Bryan Freedman, have accused Los Angeles County District Attorney Nathan Hochman of bias and violating the family's rights.
"This is a DA who made up his mind and did no hard work in terms of his position," Mr Geragos said after the hearing. He also accused several members of the prosecution of conflicts of interest.
