By Susan Cornwell

WASHINGTON, Jan 11 (Reuters) - Roland Burris said on Sunday he will return to Washington this week to pursue being sworn in to fill President-elect Barack Obama's vacant Senate seat before Obama is inaugurated as president on Jan. 20.

The Senate's second-ranking Democrat, Dick Durbin, said the chamber would try to decide Burris' fate fairly and quickly, without waiting to see whether the embattled official who appointed Burris, Illinois Gov. Rod Blagojevich, is removed from office.

Burris told CBS' "Face the Nation" that his lawyers will be in the U.S. capital on Monday to meet the Senate parliamentarian, adding that he would follow them to Washington "in a day or two."

"It is our position that we have done everything that's required and that, yes, I should be seated and I should be seated forthwith and I should be seated prior to the inauguration of our -- our 44th president," Burris said.

"I am the junior senator from the state of Illinois. There is no question of my legality of appointment," said Burris, 71, a former Illinois attorney general.

With Obama set to be sworn in as the first black U.S. president on Jan. 20, Burris seeks to replace him as the only black member of the 100-person U.S. Senate.

But Burris was turned away from the Senate last week after the Democratic majority vowed any appointment of Blagojevich's would not stand because of accusations that Blagojevich had tried to sell Obama's seat to the highest bidder.

Blagojevich was impeached by the Illinois state House on Friday and faces a state Senate impeachment trial that could remove him from office. But Burris told an Illinois committee he had made no deals to gain the appointment.