The executive order directs department leaders to come up with a comprehensive strategy for the higher wage for city employees.
"We want to serve as a model to make Seattle a city where individuals and families are paid livable wages," Murray tweeted Friday.
A preliminary budget analysis shows the move would cost Seattle about $700,000 in additional payroll and benefit costs. Murray spokesman Jeffrey Reading said the costs could rise, depending on factors such as union provisions.
About 600 city workers now earn less than $15 an hour, including ushers, cashiers and attendants. There are about 10,000 city employees.
The move to a higher wage for city workers would likely require additional budget authority, which would need to be approved by the City Council, said budget director Ben Noble.
Murray, a former state senator who won the mayoral election with about 52 percent of the vote, campaigned on hiking the city's minimum wage to $15 an hour by the end of his four-year term. He took office Jan. 1 and made the wage announcement at his first news conference.
He recently created an advisory group to come up with the best plan for increasing the minimum wage in the private sector. The group would study the impact of raising the minimum wage for businesses of various sizes.
"This is a negotiation. The outcome is not predetermined," Murray tweeted after someone on Twitter worried that a $15 minimum wage would kill local businesses.
On Jan. 1, a $15 minimum wage kicked in for about 1,600 hotel and parking lot workers in the city of SeaTac, south of Seattle, after voters approved a city initiative. However, the pay hike didn't take effect for about 4,700 workers because a King County judge struck down part of the measure that applied to employees and contractors working within Seattle-Tacoma International Airport, which is operated by the Port of Seattle.
Initiative supporters have appealed the judge's decision to the state Supreme Court.