SAN JOSE — After being called out by neighboring cities for not following through on an idea to raise wages regionally, San Jose leaders Tuesday agreed to raise the minimum wage to $15 by January 2019 — but decided to exclude youth in job training programs from the higher wage.

The unanimous vote Tuesday will bump the city’s minimum wage to $12 on July 1, 2017, and $13.50 on January 1, 2018, before reaching $15 on January 1, 2019. San Jose’s current $10.30 minimum wage goes up by twenty cents this January.

The discussion drew passionate pleas from both sides — business owners who said labor costs are engulfing their profits and low-wage earners who said they’re barely surviving after paying rent and bills in one of the nation’s costliest cities.

At the heart of the issue was whether to allow exemptions from the higher minimum wage to certain “hard-to-employ” populations to motivate companies to hire them.

San Jose Mayor Sam Liccardo earlier this year led the charge to raise the pay floor regionally to avoid a patchwork of wages across city borders. San Jose and 12 other cities in June endorsed a plan from the Cities Association of Santa Clara County to reach $15 by January 2019 with no exemptions.

But Liccardo last week issued a proposal, co-signed by Vice Mayor Rose Herrera and Councilmen Chappie Jones and Manh Nguyen, to wait until July 2019 to reach $15 and to exclude youth in jobs programs for 120 days.

The council agreed to the youth exemption under Liccardo’s plan. No other Silicon Valley city has such exemptions. Neighboring city leaders cried foul, claiming San Jose backed out of its promise to lead the regional approach.

“We’ve worked together on so many things and we welcome San Jose’s leadership, but we expect them to follow through and be consistent,” said Cupertino Councilman Rod Sinks.

The cities of Los Altos, Palo Alto and Cupertino have adopted ordinances to reach $15 by January 2019. Mountain View and Sunnyvale have agreed to reach $15 sooner, by 2018. “We followed San Jose,” said Mountain View Councilwoman Margaret Abe Koga. “This time it’s San Jose’s turn to follow us.”

Kim Walesh, San Jose’s economic development director, suggested the city adopt a $15 minimum wage a year later than its neighbors — by January 2020 — to avoid consequences on businesses.

Business and nonprofit leaders said the extra time would help them prepare for the wage hike.

“We simply ask that you consider a delayed implementation date to give us the opportunity to find funds to offset those costs so we’re not forced to reduce our program services,” said Trish Dorsey, vice president of mission services at Goodwill of Silicon Valley.

But dozens of minimum wage earners urged elected leaders to consider their plight. A city-sponsored study found 115,000 San Jose workers would benefit from the wage increase, earning an extra $3,000 a year.

“All I have in my wallet right now is $50. It’s a day-to-day struggle,” said Yasmin Fernandez, 33, who works at Panda Express and a gas station, through a Spanish interpreter. “I work two jobs and the rent is going up. My family is suffering and I can’t make ends meet.”

Council members Magdalena Carrasco, Raul Peralez, Ash Kalra and Donald Rocha supported no exemptions, saying the minimum wage increase should benefit everyone, but ultimately compromised on the youth exemption.

Kalra said the city needs to “start sympathizing with our community and how hard it is out there.”

“Many of these people are supporting their families and, if anything, they need that money more than anyone,” Kalra said.