"A significant change in the scope of the problem" forced the mayor to put off his goal, spokeswoman Connie Llanos said. "The mayor's commitment to housing homeless veterans is stronger than ever."
The L.A. region has long had the largest concentration of homeless veterans in the country — 4,343, two-thirds of whom live in the city, according to the official count in January.
The delay was first reported by the Los Angeles Daily News, which said the mayor told its editorial board that fulfilling his commitment could take until "the beginning of the summer" of 2016.
Garcetti took the pledge a year ago during a high-profile appearance with First Lady Michelle Obama at the Hyatt Regency Century Plaza.
More than 700 other local officials, including 585 mayors, joined the first lady's challenge to rid the streets of homeless veterans, a national priority of the Obama administration. Several cities have claimed success, including New Orleans, Salt Lake City and Phoenix.
In January, the mayor said he was more than halfway there, but the count conducted that month and released in May showed a 6% increase in the city's veteran homeless numbers.
Llanos said the rise was "substantially larger" than estimates from both the mayor and homelessness experts, and came despite significant advances in helping veterans.
Los Angeles housed 3,733 veterans from January to June, "more than Salt Lake City, Phoenix, Houston and New Orleans combined," she said.
Llanos said the city is not "attributing [the jump] to a specific reason" but added the soaring rents and restricted housing stock have created a housing crisis.