Libby's lawyers said they would base their appeal on the contention that the special prosecutor, Patrick Fitzgerald, was improperly appointed.
They also plan to argue that Reggie Walton, the presiding district judge, was wrong to exclude witnesses and classified material Libby had hoped to use in his defence.
Walton, however, said on Thursday the appeal was unlikely to be successful.
"I would have to conclude that although he doesn't pose a danger to the community and he doesn't pose a risk of flight ... there is not a likelihood of success," Walton said.
Libby's wife, Harriet Grant, wiped away tears upon hearing the ruling but her husband remained impassive.
Both Libby and Fitzgerald left court without speaking to reporters.
After a month long trial in March, jurors found that Libby lied to investigators about how he learned that Valerie Plame, the wife of an outspoken Iraq war critic, worked for the CIA, and whom he told.
Libby was also convicted of obstructing Fitzgerald's inquiry into the 2003 identity leak.
Walton never appeared to waiver from his opinion that a delay to serving the sentence was unwarranted.
After 12 prominent law professors filed documents supporting Libby's request, the judge dismissed it as "not something I would expect from a first-year in law school".
He also said he received several "angry, harassing, mean-spirited" letters and phone calls after he sentenced Libby but said they wouldn't factor into his decision.
Libby's supporters have called for Bush to wipe away the convictions. The president publicly has sidestepped pardon questions.