In its first eight days, General Motors Co.’s compensation program has received about 120 claims, more than half of which involved deaths allegedly linked to GM cars that were recalled earlier this year to fix an ignition-switch defect, reported The Wall Street Journal.

Kenneth Feinberg, the lawyer hired by GM to oversee the program, said of the claims filed so far, about 65 were reported by families who say the victims were killed in accidents involving cars that were subject to the 2.6-million-car recall.

Another dozen claims involved catastrophic injuries and the remaining are from people who were hospitalized, Mr. Feinberg added.

“We are just beginning now to review the claims and the documentation, to see whether they are eligible,” Mr. Feinberg said Friday. “It will be well after Labor Day before we begin to draw some conclusions,” he added. “We are encouraged by the early filings. It’s a good sign that owners are aware of the program and understand the program.”

The closing date to file isn’t until the end of the year.

The initial tally raises questions about whether GM has underestimated the number of deaths linked to the defect, which GM knew about for more than a decade but didn’t recall the cars to fix until February.

The company attributes at least 54 crashes and 13 deaths to faulty ignition-switches, which can abruptly slip out of the “on” position, stall the car and disable the air bags.

GM’s compensation plan will offer payouts for any accident in which the cars’ air bags failed to deploy. The checks could range from $20,000 to several million dollars to any driver, passenger, pedestrian or occupant of another vehicle, who can show they were hurt in a crash involving GM cars recalled this year for the defective ignition switch.

A death would automatically be awarded $1 million for pain and suffering above any other payments.

The program has no overall dollar limit, but a key condition is claimants must show via police or other reports a vehicle’s air bag didn’t deploy in the crash.

Any out-of-court death settlements connected to ignition-switch litigation can be refiled.

Mr. Feinberg said that once a victim’s application is deemed eligible, and the documentation is completed, the fund will issue a payment within 90 days for simple cases and 180 days for more complicated ones.

Meantime, GM’s troubles with safety recalls resurfaced this week, with more ignition-key trouble and a group of sport-utility vehicles requiring fixes to power-window switches because they might catch on fire. GM is telling customers to park the SUVs outside until they are repaired.

The power-window recall involves about 189,000 vehicles in North America, mainly from the 2006 and 2007 model years. Models affected include the Chevrolet TrailBlazer, GMC Envoy, Buick Rainier, Isuzu Ascender and Saab.

GM also announced the recall of 202,115 Saturn VUEs because the ignition key can possibly be removed when the vehicle isn’t in the off position.

GM also recalled 48,059 2013 Cadillac ATS four-door sedans and 2013 Buick Encore vehicles because of lap-belt issues; 14,940 2014-2015 Chevrolet Impala sedans because of potential problems with the front-console storage compartment; 1,968 2009-2010 Chevrolet Aveo and 2009 Pontiac G3 vehicles for a brake-fluid issue; and 1,919 2014 Chevrolet Spark for potential bolt issues.