Among other things, the bill requires gun owners to register their weapons every three years and receive training by a certified firearms instructor.
"This bill will be, I think, one of the most progressive registration laws in the country," Council member Phil Mendelson said.
The National Rifle Association accused the city of forcing residents to jump through unnecessary hurdles, thereby undermining the intent of the Supreme Court's ruling in June that affirmed the right of Americans to keep guns in the home for self defense.
"The D.C. Council continues to try to make it harder and harder for law-abiding citizens to access this freedom," NRA Executive Vice President Wayne LaPierre said.
In September, the House passed an NRA-backed bill that would have essentially stripped the city of its ability to regulate firearms, but the measure died in the Senate.
D.C. leaders say they are trying to be respectful of the Supreme Court case while doing everything they can to enact strict gun control measures in a city where gun violence is common.
"No constitutional right is absolute, nor is this right to possess a gun in the home for self defense," said councilwoman Mary Cheh, a law professor at George Washington University.
Since the handgun ban was overturned, the council has passed legislation allowing residents to own most semiautomatic pistols while banning magazines capable of firing more than 10 rounds. Registration also is limited to one pistol a month, and gun owners face prosecution if they fail to keep loaded weapons away from children.
Tuesday's bill builds on those regulations. It requires gun owners to spend at least one hour at the firing range and four hours in the classroom with an instructor before registration. The bill also requires a criminal background check for gun owners every six years.