Carol Hunstein made the remarks in the state of the judiciary address, her first as the Georgia Supreme Court's chief justice, before a joint session of the state Legislature.
Hunstein said the court system's backlog has grown as state money flowing to the judicial branch has dwindled.
The problem is particularly pronounced in the state's superior courts, which handle criminal cases.
In the past five years, Hunstein said, superior court caseloads have jumped 20 percent and the appointment of new judges has failed to keep pace. Data indicate Georgia has a shortfall of 72 superior court judges, she said.
A Republican state senator last week proposed cutting 19 superior court judges for a savings of up to $14 million. Mitch Seabaugh argued the superior court system has not borne its share of the burden during the state's budget crisis and has made far fewer cuts than many other departments. The plan has failed to gather much support.
Georgia has been grappling with 15 consecutive months of declining tax collections.
Hunstein said Georgia's judicial branch received less than 0.8 percent of the total state appropriations in 2009. That's the judiciary's smallest share of state appropriations in recent history and comes as the state's population and needs have grown, she said.
"The need for justice does not diminish with a shrinking economy," Hunstein said. "Indeed as our caseloads attest, it grows ... our citizens suffer when business and personal disputes are not heard and resolved. Our public safety is at risk when crimes are not prosecuted, and criminals are not punished."
Hunstein said the constitutional requirement for speedy trials in criminal cases is posing a threat to civil cases, which have been placed on the back burner. She said one judge had to suspend all civil jury trials for six months. In some parts of the state, it takes up to two months to get a hearing in a temporary child custody case -- a process that used to take a couple of weeks.
"At the state's highest court, our operating budget has shrunk so low that we had to return a copy machine that we desperately needed," she said.