Northwest Public Radio reported Inslee said Tuesday night he thought his lead would hold up.
"I believe tonight our state has taken another step forward and we have elected a forward looking governor and I fully intend to be that governor for the state of Washington," Inslee said.
McKenna said he wasn't ready to concede and asked his supporters to hold on, possibly a few more days, Northwest Public Radio said.
"We are confident that thanks to your hard work and dedication that when the last ballots are counted it will be clear that voters have sent a clear message that it is time to move our state in a new direction," McKenna said.
U.S. Sen. Maria Cantwell, D-Wash., won re-election Tuesday and Washington voters also approved a marijuana legalization measure.
Washington went Democratic Tuesday by sending Cantwell back to Washington and handing President Obama a dozen electoral votes.
A ballot measure decriminalizing marijuana possession and regulating its cultivation passed Tuesday with 55 percent of the vote and 51 percent of the ballots counted.
Cantwell cruised past Republican challenger Michael Baumgartner with 59 percent of the vote.
The Democrats captured six of the 10 House seats up for grabs. The GOP won the other four.
A ballot measure that would legalize same-sex marriage but also allow clergy and churches to refuse to perform marriage ceremonies for homosexuals or recognize the unions was heading toward passage by about a 52-48 margin.