The group known as 15 Now must collect more than 30,000 signatures to make the November ballot.
The number is seemingly within reach following election wins last year by candidates who supported a wage hike, including Kshama Sawant, a socialist who clinched a council seat from an incumbent. Sawant is a leader of 15 Now.
The group is pursuing a city charter amendment so it could not be changed by the City Council at a later time.
"It's putting the power in the hands of citizens of Seattle where it belongs," said Jess Spears, a 15 Now organizer. "The city charter needs to reflect the fundamental needs of the people."
The move marks the latest development in the minimum wage debate involving Murray, 15 Now and business interests.
Murray backed increasing the minimum wage during his campaign then created an advisory group of labor and business representatives after his election. Its recommendations will be sent to the City Council at the end of April.
Co-chair Howard Wright has said he doesn't expect the group to recommend an immediate wage hike.
Murray said he appreciated Sawant advising him in advance about the ballot measure.
"I remained committed to making progress on this issue through the stakeholder process we launched in December," he said in a statement.
Business groups had been quiet in the debate until recently. A new business coalition known as OneSeattle says it backs an increase to $15 an hour if it includes phase-ins, counting tips and commissions, and other factors.
Spears said 15 Now would drop its charter amendment effort if the City Council passes a wage hike without exemptions and without delay.
"We're practical people," she said.
It appears that 15 Now will pursue the charter amendment without SEIU 775. The labor organization - which had been providing organizers to 15 Now and directed money and people for SeaTac's minimum wage measure - is not endorsing the charter amendment. David Rolf, its president, is co-chair of Murray's advisory group.