OLYMPIA — For months, Republicans have fumed over Gov. Jay Inslee's use of a state-funded security detail while hopping through Iowa, New Hampshire and other states during his short-lived presidential bid.

Now, the Washington State Republican Party plans to deliver a petition to the Capitol campus Friday demanding Inslee reimburse the state for those costs.

Inslee ended his presidential campaign Wednesday night and announced Thursday that he's running for a third term as governor.

The petition will be delivered around noon Friday, the same time the state Republican Party has scheduled a news conference to discuss Inslee's gubernatorial campaign.

"We're demanding Inslee pay back the taxpayers and delivering nearly 5,000 petition signatures to the Governor's Office of hardworking Washingtonians who think it's time for Inslee to do the right thing!" the party wrote in a description of the event on Facebook.

Inslee's security detail is a plainclothes detachment of the State Patrol and operates like a version of the Secret Service.

Last year, even before the governor announced his presidential bid, The Seattle Times and Northwest News Network reported that Inslee's increasing travel was straining the troopers in the small unit. Between March and June, Inslee's State Patrol security detail racked up travel and overtime expenses totaling more than $580,000, according to figures released by the agency.

The two-term governor has declined to reimburse the State Patrol’s costs from his presidential campaign, saying that all governors are entitled to such protection, whether they're traveling on political or official business.

“This is a state law or obligation that security is provided, has historically been provided for any governor for all of their travels under any circumstances. I am not going to propose a change in that policy,” Inslee said during a March campaign trip to Iowa.

Chris Loftis, a spokesman for the State Patrol, told The Seattle Times in March that Inslee did not ask for bolstered security; it was a decision the Patrol made after consulting with other states that have had governors run for the presidency.

Between March 1 and the end of July, Inslee was on the road for all or parts of 90 days out of 153, or nearly 60 percent, according to an analysis of his official calendar by The Seattle Times and public radio’s Northwest News Network.

Inslee has also brushed off Republican criticism of how much his campaign travel took him away from his $182,000-a-year job as governor, saying he “can do this work anywhere there is a cellphone, and I do it.”

Information from Seattle Times archives is included in this report.