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Mayor Stephanie Rawlings-Blake at a community event in Baltimore in July.Credit Drew Angerer for The New York Times

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WASHINGTON — The family of Freddie Gray, the 25-year-old black man who sustained a fatal spinal cord injury in police custody — setting off the worst unrest in Baltimore since 1968 — reached a $6.4 million settlement with the city on Tuesday, just days before a judge is to consider whether to move the trials of six officers facing charges in his death.

The tentative settlement, which must be approved by city leaders, was reached even before the Gray family filed an expected civil suit. In making the announcement, Mayor Stephanie Rawlings-Blake said the settlement “should not be interpreted as a judgment on the guilt or innocence of the officers facing trial,” but had been negotiated to avoid “costly and protracted litigation that would only make it more difficult for our city to heal.”

But the police union pounced on the timing. The union president, Lt. Gene Ryan, issued a statement saying it was “obscene” to settle with the family before the officers went to trial.

Legal specialists said the $6.4 million was in line with settlements for recent racially charged police misconduct cases and might herald an era in which juries and city officials were inclined toward bigger payouts, given the national conversation over police treatment of African-Americans.

In July, the estate of Eric Garner, who died in New York after the police used a chokehold, a banned maneuver, to restrain him, settled with the city for $5.9 million. In Cleveland on Tuesday, just as the Gray settlement was being announced, a jury awarded $5.5 million to the estate of Kenneth Smith, a 20-year-old hip-hop artist who was fatally shot by an off-duty officer.

“It used to be that we couldn’t even get fair play in these cases because the cards were stacked against us,” said Terry Gilbert, the lawyer representing the Smith estate. “But now there is a new mood in this country because of the police shootings. People are beginning to see there are serious problems with criminal justice.”

In Baltimore, Kurt L. Schmoke, who was the city’s first elected black mayor and is now the president of the University of Baltimore, called the proposed settlement a “positive step” and said it could help calm a city that remains on edge.

“It is an admission by the city leaders that there was negligence but that they’re taking steps to heal the wounds that arose out of that negligence,” Mr. Schmoke said. “It won’t satisfy everyone, but if the family can convey a message that this is a positive step, then I think it could help defuse some of the anger that’s out there.”

A lawyer for the family, Billy Murphy, declined to comment Tuesday, but he scheduled a news conference for Wednesday. The city Board of Estimates, a five-member panel, including the mayor, that approves purchases and contracts, will consider the proposal on Wednesday and is likely to approve it.

The proposed settlement comes as judicial hearings are beginning against the six officers facing criminal charges in the case. Last week, Judge Barry G. Williams of the Baltimore City Circuit Court ruled that the six would be tried separately; on Thursday, the judge will consider a request by defense lawyers to move the trials outside Baltimore.

The agreement with the Gray family may help the defense make that case, said Ekow N. Yankah, a professor at the Cardozo School of Law: “They will argue that the normal jury is going to think that the city’s settlement is in some way an admission of guilt.”

In filing criminal charges against the six officers, the state’s attorney for Baltimore City, Marilyn J. Mosby, has asserted that on April 12 they improperly arrested and shackled Mr. Gray, flouting police rules and standards of decency by loading him into a police van without required safety restraints and ignoring his pleas for help during the ride.

The six face varying charges. Officer Caesar R. Goodson Jr., the driver of the van, is charged with second-degree depraved-heart murder — in essence, murder with willful disregard for human life. Sgt. Alicia D. White, Lt. Brian Rice and Officer William G. Porter are charged with manslaughter. Officers Edward M. Nero and Garrett Miller face lesser charges, including second-degree assault.

By Baltimore standards, the proposed settlement may seem large. Last year, The Baltimore Sun reported that taxpayers had paid $5.7 million since 2011 in judgments or settlements in 102 lawsuits claiming police misconduct. But Professor Yankah said those settlements were capped under Maryland law, and had the Gray family filed a civil suit in federal court — where the caps do not apply — Baltimore could have faced a judgment in the millions.

“This case is happening in a very particular, very racially charged time, where the whole country is looking at police violence and minority relationships,” he said. “The mayor would be deeply irresponsible not to take into account the current climate.”