Washington  - US Vice President Dick Cheney on Thursday welcomed vice president-elect Joe Biden to his official residence at the Naval Observatory in north-west Washington DC.

The meeting followed Monday's exchange between president-elect Barack Obama and President George W Bush at the White House, as part of the transition process.

As Obama prepares for inauguration on January 20, he announced Thursday that he would be resigning his US Senate seat, effective Sunday.

"It has been one of the highest honours and privileges of my life to have served the people of Illinois. ... In a state that represents the crossroads of a nation, I have met so many men and women who've taken different journeys but hold common hopes for their children's future," Obama said in a statement.

"It is these Illinois families and their stories that will stay with me as I leave the United States Senate and begin the hard task of fulfilling the simple hopes and common dreams of all Americans as our nation's next president."

At Thursday's private meeting, Biden was accompanied by his wife, Jill, who also met with Cheney and his wife, Lynne, for a tour of their future residence.

It was a potentially awkward encounter. During the vice- presidential debate on October 3, Biden said that Cheney "has been the most dangerous vice president we've had probably in American history."

"The idea he doesn't realize, that Article I of the Constitution defines the role of the vice president of the United States, that's the executive branch. ... The idea he's part of the legislative branch is a bizarre notion invented by Cheney to aggrandize the power of a unitary executive, and look where it has gotten us. It has been very dangerous," Biden said in the televised debate, which was viewed by more than 70 million people.

There were no details of the Biden-Cheney private meeting, with only an official photograph to be released late Thursday.

"The Bidens thank the Cheneys for welcoming them into their home and for their gracious hospitality," said Elizabeth Alexander, spokeswoman for the vice president-elect.

The white mansion, built in 1893 for the superintendent of the United States Naval Observatory, was so lovely that the chief of naval operations made it his home in 1923. In 1974, Congress voted that Number One Observatory Circle would be the official residence of the vice president.

On election day, November 4, as Biden awaited the results, he told reporters that his grand-daughter Finnegan, 10, would like it if he stayed at the Naval Observatory, as it was only about 3 kilometres from her home. (dpa)