The party also headed to the state Supreme Court on Friday to seek a ruling that all ballots be treated the same from county to county. That would mean considering some previously uncounted ballots, particularly in Democratic-leaning King County.
Chief Justice Gerry Alexander said the court may hear oral arguments next Wednesday or Thursday.
The Democrats' twin actions ensured that the election, already entering its second month, will last at least until Christmas week. The recount will be ordered by the secretary of state on Monday.
Democrat Christine Gregoire, 57, best known for her successful battle with the tobacco industry as the state's three-term attorney general, trailed Rossi, 45, a former state Senate budget chairman, by just 42 votes after a machine recount was certified earlier this week.
The new recount will be done manually.
Rossi won the initial vote count by 261 ballots, a margin so close it triggered the mandatory machine recount.
"This really is sad and desperate," Rossi said in an interview. "How much do they want to put the voters of Washington through? We were elected and certified twice. I have faith in voters; Christine Gregoire has faith in lawyers.
"She doesn't like the results the voters came up with and now she want to redefine how we run elections."
"It sounds like they want to make Florida look like a tea party," complained Mary Lane, a Rossi spokeswoman.
"We are not going to let this stand. We will not let her try to steal this election."
Rossi held forth at a news conference in Bellevue, but Gregoire stayed out of sight, working on transition plans in Olympia.
"It may take a few more weeks, but it will be worth it for four years of legitimacy," she said in a statement.
In an interview, she said, "We're just doing what state law allows, but then it's over. That will put this thing to rest."
Democrats are more interested in getting new ground rules than in the statewide recount, said state GOP Chairman Chris Vance.
"We're into a street brawl. It's bad for the system. We're now way off the map. We're into the political Twilight Zone. Democrats are breaking every rule of politics and by doing this, Christine Gregoire has forfeited any chance she had to be considered legitimate if she were to win.
"This is an Armageddon-type process."
But Gregoire was delighted that donors flooded the state party with enough money to pay for the full recount, rather than just a partial recount in some counties. A day earlier, she had threatened to concede if the party counted only hand-picked counties.
"We have a thoughtful system of counting every vote in Washington state, and over the next few weeks, we will see it work," she said. "With the election too close to call, a hand count will finally determine the winner."
State Democratic Chairman Paul Berendt said the party gave the secretary of state's office a cashier's check for $730,000 to order a recount of all 2.9 million votes cast for governor on Nov. 2 - not just votes in selected counties. A flood of online contributions this week allowed the party to pay for the hand count.
"We're going to count every vote in every county, whether it's a Rossi county or a Gregoire county," Berendt told a Seattle news conference, flanked by outgoing Gov. Gary Locke and former Gov. Booth Gardner, both Democrats and mentors of Gregoire's.
"Our representatives are also filing with the Supreme Court to make sure every vote will be counted and that every ballot will be treated the same in every county throughout the state," Berendt said.
He referred to hundreds of questioned ballots, including provisional ballots and absentee votes, that were rejected by some counties.
The hand count is expected to cost the party more than $1 million, including legal costs, and leaders said it was a backbreaking job to raise that kind of money in just a week.
Sen. John Kerry, the party's unsuccessful presidential nominee, donated $250,000 in surplus campaign contributions and the Democratic National Committee and Moveon.org contributed similar amounts. EMILY's List, a national campaign group for pro-choice Democratic women, contributed, as did more than 10,000 individual donors, many online, the party said.
The party's fund raising topped $1 million by Friday night, including donations prompted by an appeal by Howard Dean, said party spokeswoman Kirstin Brost.
Secretary of State Sam Reed said he will order the new count on Monday and counties are expected to begin the laborious job Wednesday or Thursday. Reed said the count should be completed by Dec. 23 unless there are legal challenges.
The chief justice said the party is suing Reed, King County and its election chief, and Franklin, Pierce and Pend Oreille counties.
"It's a mandamus action asking us to order him (Reed) to make certain rules and regulations" to guide the recount, Alexander said in an interview. "The big nub of the case is, should we order them to recount the previous votes or recount those votes plus those that supposedly should have been counted?"
The high court is scattered for the holidays, but at least five justices will likely hear the case. The two sides have hurry-up briefing deadlines on Tuesday and if the court grants a full hearing, that would be on Wednesday or Thursday, Alexander said.