President-elect Barack Obama named Sen. Hillary Rodham Clinton (D-N.Y.) as his secretary of State on Monday.

He tapped for the most visible national security position his opponent in the long, costly and bitter Democratic presidential primary in which her campaign raised questions about his competence to handle a major foreign policy crisis.

Obama, who appeared with Clinton at a Chicago news conference, also made a significant down payment on his pledge to include Republicans in his administration, saying Defense Secretary Robert Gates will stay in his job. He also announced the rest of his national security team, naming Democratic Arizona Gov. Janet Napolitano as secretary of Homeland Security, Gen. James Jones to be national security adviser, Eric Holder to be attorney general and Susan Rice as the U.S. ambassador to the United Nations.

Obama brushed aside past differences with Clinton and the others, saying the group shares “a core vision” and noting he wants spirited debate among his advisers. He accused a reporter of “having fun” for asking about suggestions by his campaign during the presidential primary that Clinton lacked real foreign policy experience.

Instead, Obama was effusive in his praise for the former first lady, calling her “an American of tremendous stature who will have my complete confidence” and referring to her as “my dear friend.” He said there was no single “light bulb” moment at which it occurred to him to make her secretary of State, but otherwise declined to describe his selection process.

Clinton, whose presidential campaign ran the famous “3 a.m. commercial” suggesting Obama was ill-prepared to respond to an early morning crisis phone call, today thanked the president-elect for the opportunity. She also thanked her constituents in New York, saying that leaving the Senate “is very difficult for me.”

Clinton’s Senate replacement remains unclear. New York Gov. David Paterson (D), who will appoint her successor, has given no indication of whom he might name or when an announcement will be made.

The list of potential appointees includes no fewer than nine House Members, along with state Attorney General Andrew Cuomo (D), Buffalo Mayor Byron Brown (D), Nassau County Executive Tom Suozzi, environmental attorney Robert F. Kennedy Jr. and Clinton’s former Senate counsel Leecia Eve.

Praise abounded from Capitol Hill for Obama’s national security team picks, including from Speaker Nancy Pelosi (D-Calif.), who said his choices send “a message of confidence.”

Pelosi said she called Clinton this morning to congratulate her on her upcoming role. The Speaker refrained from endorsing either candidate during the Democratic presidential primary standoff between Obama and Clinton earlier this year. However, she made comments on several occasions suggesting a tilt toward Obama.

Jennifer Bendery and Josh Kurtz contributed to this report.