U.S. President George W. Bush arrives in the Rose Garden of the White House to make a statement congratulating president-elect Barack Obama. (Ron Edmonds/Associated Press)

Barack Obama's election victory represents a "triumph of the American story" that fulfilled a dream for millions of people and made every American proud, U.S. President George W. Bush said in a congratulatory speech Wednesday.

Speaking in the White House Rose Garden the day after the U.S. election, Bush, a Republican, said he had a "warm conversation" with the Democratic president-elect to congratulate him on the resounding win.

"I told the president-elect he can count on complete co-operation as he makes the transition to the White House," said Bush.

Obama will be sworn in as the 44th president of the U.S. on Jan. 20.

Bush said he also spoke with Arizona Senator John McCain and Alaska Gov. Sarah Palin, the Republican presidential and vice-presidential candidates, to congratulate them on their "determined campaign."

"The American people will always be grateful for the lifetime of service John McCain has devoted to this nation."

His speech focused, however, on the historical significance of the victory by the 47-year-old African-American senator from Illinois.

"No matter how they cast their ballots, all Americans can be proud of the history that was made yesterday.

"This moment is especially uplifting for a generation of Americans who witnessed the struggle for civil rights with their own eyes," he said. "And four decades later, to see a dream fulfilled."

Bush said the record voter turnout, with as many as 136.6 million ballots cast, showed the world the "vitality" of America's democracy.

"[Voters] chose a president whose journey represents a triumph of the American story, a testament to hard work, optimism and faith in the enduring promise of our nation."

Rice 'especially proud'

In a speech in Washington, Secretary of State Condoleezza Rice also spoke about the significance of Obama's election, calling it an "extraordinary step forward" in efforts to overcome racism.

"As an African-American, I'm especially proud," Rice told reporters at the State Department.

America "continues to surprise," Rice said. "You just know that Americans are not going to be satisfied until they really do form that perfect union. And while the perfect union may never be in sight, we just keep working at it and trying."

Rice pledged that the State Department would work to make sure the transition to an Obama administration is smooth.

She called Obama "inspirational" and said that McCain was "gracious" and a "great patriot."

Historic win in House of Representatives: Pelosi

Later in the day, House Speaker Nancy Pelosi hailed Obama's victory and said the American people spoke "loudly and clearly" for change in the country.

The California Democrat said the party's back-to-back gains in the House of Representatives in both the 2006 mid-term election and Tuesday's vote were remarkable.

"This is historic, that you would have one wave after another. It's a signal of the change the American people want," said Pelosi.

The Democrats made gains in both chambers of Congress, with five extra seats in the Senate and about 25 more in the House of Representatives. Not all the winners had been called by midday Wednesday.

Pelosi also repeated her call for a session of Congress to be held before Obama's swearing in to enact a stimulus program to help shore up the sinking economy.

She said no decisions have been made on such a post-election session, but talks are continuing with the White House on terms of such a package, which would include additional assistance for people who are out of work.

Obama gets to work

Meanwhile, the president-elect was hard at work in Chicago putting together a transition team and making decisions about key cabinet posts.

He reportedly offered the White House chief-of-staff job to longtime confidant, Illinois Representative Rahm Emanuel, hours after his victory. The Democratic congressman and veteran of President Bill Clinton's White House was apparently considering the offer.

Obama faces enormous challenges when he takes office in 2½ months, with the United States dealing with a sputtering economy and costly involvement in the two major conflicts in Afghanistan and Iraq.

"Winning was the easy part," Willis Sparks, a political risk analyst with the Eurasia Group, told CBC News. "The reaction around the country last night, it was like the Berlin Wall fell."

"But tomorrow he's going to get his first intelligence briefing, and in the foreign policy sense, he's going to see exactly how daunting the challenges are and how many of them there are right away."

Sparks praised Emanuel as the "perfect choice" for the chief of staff post, describing him as a "power broker in the U.S. House of Representatives where Obama is certainly going to need some allies."

He warned, though, that the change Obama promised throughout the lengthy election campaign may be "on hold" for the first few months, as he faces pressure to bring familiar faces in to restore confidence in the U.S. economy.

With files from the Associated Press