A declaration would provide federal assistance to help families, business owners and local governments recover from the wildfires.
Inslee sent a letter to the Federal Emergency Management Agency, asking for federal aid for Chelan and Okanogan counties and the Confederated Tribes of the Colville Reservation.
That covers the areas hardest hit by wildfires so far this summer. That includes the Carlton Complex, the largest wildfire in state history.
An estimated 323 homes have been destroyed in Okanogan County this fire season, Inslee said.
"The people of Chelan and Okanogan counties and the Colville Reservation are resilient, but at the same time, their governments' resources can only go so far," Inslee said. "Federal assistance is needed."
Several large fires continue to burn in Washington.
The Devil's Elbow Complex on the Colville Reservation has burned across about 10.9 square miles, or 7,000 acres. Residents of about 25 homes have been told to evacuate. Fire spokeswoman Karen Ripley said late Wednesday that no homes have burned. About 210 firefighters are attacking the flames.
The Snag Canyon wildfire near Ellensburg in central Washington has grown to 10 square miles and is being fought by about 450 firefighters. That fire has destroyed eight homes and threatens 179 structures.
Both of the state's U.S. senators and two House members sent a letter to Obama on Thursday asking him to grant Inslee's disaster request. That letter was signed by Democratic U.S. Sens. Patty Murray and Maria Cantwell and Republican U.S. Reps. Doc Hastings and Dave Reichert.
"A disaster of this magnitude requires long-term federal assistance to help these communities respond, rebuild, and cope with this tragedy," their letter said.
The disaster assistance sought by Inslee would:
Provide funds for up to 18 months to people whose residences were heavily damaged or destroyed, so they can find temporary housing in the local area.
Provide grants to help people deal with needs not covered by insurance and other aid programs. These include replacement of personal property, transportation, medical, dental and funeral expenses.
Unemployment insurance payments to people who became unemployed as a result of the disaster.
Low-interest loans for homeowners and renters to cover uninsured property losses.
In addition, Inslee is asking for federal funds to repair roads, bridges, public utilities and other public infrastructure. Preliminary assessments show the fires caused about $35 million in such damages.