Murray, a Democrat, pitched his plan as a compromise between supporters of a more immediate wage hike and concerned business owners. It was crafted by a panel he appointed that includes both business and labor leaders.
"Throughout this process, I've had two goals: to get Seattle's low-wage workers to $15-per-hour while also supporting our employers, and to avoid a costly battle at the ballot box between competing initiatives," Murray said. "We have a deal that I believe accomplishes both goals."
Critics say the plan takes too long to phase in for many workers.
"This proposal does not live up to the wishes of Seattle's workers," said city council member Kshama Sawant, who served on the mayor's panel but opposes the plan. "Unfortunately it also reflects the attempts of business to water down what the working people want."
Both Sawant, a socialist, and Murray won their seats in November campaigning ona $15 minimum wage.
Voters in nearby SeaTac approved a $15 minimum wage in November, but many workers there haven't yet seen the increase. The law is currently tied up in court over whether it applies to the Seattle-Tacoma airport, which employs many of the community's workers.
Several states have passed or are considering proposals to adopt a $10.10 an hour wage, the level that many congressional Democrats and President Obama want to see passed through Congress. But an attempt to do that failed in the Senate this week. The federal rate has not increased since 2009.
-- CNNMoney's Jeanne Sahadi contributed to this report