HARVEY, Ill.—Many politicians have called recently for new laws to prevent criminals and the mentally ill from obtaining guns. But in some parts of the U.S., the focus has turned to confiscating firearms from the convicts and mentally ill who already have them.

Under federal and most state laws, legal gun owners lose their right to possess firearms when they are convicted of a felony or violent misdemeanor, or are judged by a court to be mentally ill. Officials tell these people they must surrender their guns, but in much of the country, authorities don't ensure they do. Instead, people who are prohibited from having guns are left to get rid of them on their own.

Now some officials are accelerating efforts to seize those firearms. In recent months, the sheriff of Cook County, which includes Chicago, launched a gun-confiscation program; California began adding agents assigned to take away firearms; and New York enacted a law that paves the way for such a program.

On a recent Wednesday here in the rundown suburbs south of Chicago, five police officers with bulletproof vests and Glock handguns knocked on doors and tried to talk their way into homes of felons and mentally ill residents who, according to records, held gun licenses.

In its first six months, the unit has confiscated nearly 200 guns, but it has almost 5,000 more names to check.