Murray said Indiana's new law "doesn't reflect the values" of Seattle.
"This is why I am ordering that none of our taxpayer dollars should go toward supporting this discriminatory law," Murray's statement continued.
Supporters of the law say it prevents the government from compelling people to provide services such as wedding photography for same-sex weddings or other activities they find objectionable on religious grounds.
"This bill is not about discrimination," Pence had said, "and if I thought it legalized discrimination I would have vetoed it."
In an interview today with the Indianapolis Star, Pence said he will support legislation to clarify the law.
"I support religious liberty, and I support this law," Pence said. "But we are in discussions with legislative leaders this weekend to see if there's a way to clarify the intent of the law."
But hundreds of people gathered outside of the Indiana Statehouse on Saturday, some carrying "no hate in our state" signs, to rally against the law.
Consumer review service Angie's List also said today that it is suspending a planned expansion in Indianapolis because of the new law.
Angie's List had sought an $18.5 million incentive package from Indianapolis' City-County Council to add 1,000 jobs over five years. But founder and CEO Bill Oseterle said in a statement that the expansion was on hold "until we fully understand the implications of the freedom restoration act on our employees."
The Associated Press contributed to this report.