California Republicans have been collecting ballots from voters in unofficial ballot drop boxes.
Becerra is investigating to see if these drop boxes comply with state law.
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Last week, Becerra ordered Republicans to disclose the location of the boxes and the names and contact information for voters who have used them. He sued when Republicans refused.
On Wednesday, Becerra's office asked a judge to expedite the case. But Sacramento Superior Court Judge David Brown rejected the request, saying Becerra's office had not shown "immediate harm or irreparable injury."
Becerra and Secretary of State Alex Padilla, both Democrats, said the drop boxes are illegal and ordered Republicans to remove them. They worry voters will confuse the Republican boxes with the official ballot drop boxes put in place and monitored by county election officials.
However, California Republican Party General Counsel Tom Hiltachk said last week that the boxes comply with California's ballot harvesting law that allows people to collect ballots from voters and return them to county election offices to be counted.
To find early voting and vote-by-mail ballot drop off locations, visit https://caearlyvoting.sos.ca.gov/ and to make sure your vote is counted, visit https://wheresmyballot.sos.ca.gov/.
The Associated Press contributed to this report.