After he learned he could not repair an old hunting rifle he inherited from his grandfather, Bob McClure tucked it away in his Inverness home. The next time he picked up the more than 100-year-old .22-caliber Remington, it was to hand it over to law enforcement officers.

“It’s not dependent and it’s not accurate,” Mr. McClure said this week after turning in the gun to the sheriff’s substation in Point Reyes Station. “It doesn’t do me any good.”

Point Reyes was one of five sites in the county to which gun owners turned out on Tuesday, when authorities collected hundreds of firearms as part of Marin’s first gun buyback effort. It was so successful, said Marin County District Attorney Ed Berberian, who headed the effort, that each site ran out of money within hours of beginning the turn-ins, which ran from 11 a.m. to 8 p.m.

“We just frankly did not know what type of response we’d get,” Mr. Berberian said. 

The effort, emerging against the backdrop of the school shooting in Connecticut last month, was funded by donations collected by the District Attorney’s office. Authorities offered $200 for semi-atomic guns, such as assault rifles, and $100 for other types of firearms, like pistols. 

At the Point Reyes substation, which collected a total of 50 guns and 100 rounds of ammunition, including a fully automatic military rifle with a drum magazine, authorities ran out of money by early afternoon. The same occurred at the other four sites, including San Rafael and Novato police departments, St. Andrew Presbyterian Church in Marin City and a Larkspur substation.

“We were thinking the money would last longer,” San Rafael police spokeswoman Margo Rohrbacher said. More than 20 cars were seen lining the sidewalk in the morning before authorities started collecting guns outside the police department, she said, which had doled out its money by noon.

To gun owners still willing to hand over their firearms, authorities issued vouchers, totalling about $70,000, which the District Attorney’s office agreed to offer compensation—if it can raise enough money within 30 days.  

Another turn-in was originally scheduled for Monday at San Rafael and Mill Valley police departments, though the District Attorney’s Office, seeking to raise more money, plans to issue an update today.

A total of 827 guns, ranging from antique single-shot revolvers to modern pump-action shotguns and semi-automatic rifles, were collected on Tuesday, and will be sent away for incineration in coming weeks.

The program was open to residents from Marin, Sonoma, San Francisco and Contra Costa Counties, and also accepted violent video games, like Call of Duty and Grand Theft Auto, though only two were reported by authorities.

The idea of a buyback program came into focus just over a month after the deadly elementary school shooting in Newtown, Conn., in which a 20-year-old man armed with semi-automatic pistols and a high-powered rifle killed 20 children and six educators before taking his own life, and about six months after a massacre at a theater in Aurora, Colo. left 12 dead and several others wounded.

The massacres precipitated a flurry of debates over how to curb gun violence, with President Obama and other political leaders signaling for tighter gun laws.

Within days of the Connecticut shooting, Mr. Berberian met with school officials and representatives from law enforcement agencies across the county to try to “answer questions about school safety,” and drew unanimous approval from county supervisors for an effort aimed at reducing guns in homes.

“People just wanted to do something, other than just talk about it,” he said in a phone interview.

Mr. Berberian raised about $42,000 in donations in about a month, including $10,000 from the county, about $12,000 from private donors and two separate donations of $10,000 from the Marin Community Foundation, which manages trust funds from hundreds of families and businesses.

The idea resonated with Dr. Tom Peters, president and CEO of the foundation, whose more than 20 years working as chief of staff of San Francisco’s public health department saw “too many families shattered, literally shattered, by guns.”

“People are just looking for something to do,” said Dr. Peters, who views the effort as a chance to “acknowledge that this really is a moment to put aside this longstanding hesitancy, this reluctance… to do anything about guns.”

That sentiment is what led Philip and Penny Hicks on Tuesday afternoon to the Point Reyes substation, where they dropped off an old Winchester rifle they had kept in the garage of their San Rafael home.

Retired psychiatrists who over the years treated patients in cases involving guns, the Hicks were not after compensation. “The purpose of this program is to prevent gun violence,” Ms. Hicks said.

Others, though, view the effort as merely symbolic.

“There’s so many guns in the country, you couldn’t get rid of them in 10,000 years,” a 74-year-old gun owner from Marshall said outside the Point Reyes substation on Tuesday. After learning he would not receive payment, the gun owner, who requested anonymity, said he planned to hand down to his children his 12-gauge shotgun and semi-automatic rifle.

Whatever the results of the buyback program, Don Sloan of Petaluma, who drove to Point Reyes after turning away from a line of some 60 gun owners outside of the Novato police department, saw it as a way to get rid of his .22-caliber rifle and bolt-action shotgun, passed down from his grandfather who served in World War II.

Mr. Sloan, an antique gun collector, viewed the guns as “operational pieces of junk.” “There’s a lot of people who have firearms in their home… and they would like to get rid of them,” he said.