A federal appeals court Wednesday rejected former Gov. Rod Blagojevich’s bid for another shot at challenging his conviction.

The three judges on the 7th U.S. Circuit Court of Appeals who previously affirmed Blagojevich’s conviction on 13 of 18 counts voted against holding another hearing before their panel.

And none of the other active judges on the 7th Circuit voted to hold a hearing before the entire court.

One of Blagojevich’s lawyers said he would seek review before the U.S. Supreme Court.

His chances of getting a hearing before the high court are slim.

The Supreme Court receives about 10,000 petitions a year from would-be parties, but hears argument in only 75 to 80 of those cases.

Those odds, however, are better than the ones Blagojevich faced at the 7th Circuit.

Collins T. Fitzpatrick — the top administrator of the federal courts in Illinois, Indiana and Wisconsin — said an average of three of the approximately 800 cases argued before the 7th Circuit every year receive an en banc hearing.

It’s much easier, Fitzpatrick said, for litigants to get their case before the highest court in the land than before the Chicago-based 7th Circuit in an en banc proceeding.

Blagojevich is represented in the 7th Circuit by Leonard C. Goodman of Len Goodman Law Office LLC and Lauren F. Kaeseberg of the Illinois Innocence Project in Springfield.

Goodman issued a statement that he’s disappointed by the 7th Circuit’s denial.

“We believe the decision is flawed and puts every public official, who must raise campaign funds to stay in office and to be effective, at the mercy of an ambitious or politically motivated federal prosecutor,” Goodman said. “But we remain hopeful that we will prevail in the end because the decision is in conflict with established legal precedent which has existed for more than 20 years.”

The government is represented in the 7th Circuit by Assistant U.S. Attorney Debra R. Bonamici.

Spokesman Joseph Fitzpatrick of the U.S. attorney’s office declined to comment.

The case is United States v. Rod Blagojevich, No. 11-3853.

In 2011, a federal jury found Blagojevich guilty of crimes that included scheming to shake down executives for campaign contributions and trying to sell or trade the U.S. Senate seat Barack Obama left to assume the presidency.

The jury convicted Blagojevich of 17 counts that included wire fraud, conspiracy, attempted extortion and the solicitation of a bribe.

A different jury in a previous trial deadlocked on most charges, but did convict Blagojevich of one count of lying to the FBI.

U.S. District Judge James B. Zagel sentenced Blagojevich to 14 years in prison and fined him $20,000.

The sentence was much stiffer than the 6½-year term imposed on Blagojevich’s predecessor, George H. Ryan, who also was convicted of public corruption charges.

Last month, the 7th Circuit panel overturned Blagojevich’s conviction on five counts stemming from his attempt to get a Cabinet position.

The panel members — Judges Frank H. Easterbrook, Michael S. Kanne and Ilana Diamond Rovner — gave prosecutors the option of retrying Blagojevich or holding a new sentencing hearing.

Jurors would have had no basis to find Blagojevich guilty of a crime, the panel held, if they believed he tried to get a place in Obama’s administration by offering to appoint Valerie Jarrett, a friend of the then-president-elect, to the vacant Senate seat.

Such a proposal would constitute “logrolling” — a standard practice in politics, not the commission of a crime, Easterbrook wrote for the panel.

But if jurors believed Blagojevich sought money or a job in the private sector in return for the seat, he would be guilty of a criminal offense, the panel held.

U.S. Attorney Zachary T. Fardon has not yet announced whether prosecutors will seek a new trial on the five vacated counts or just proceed to a new sentencing hearing on the remaining 13 counts.

In the one-page order issued today, the 7th Circuit offered no explanation for its denial of Blagojevich’s petition for rehearing and rehearing en banc.

In addition to the three judges who served on the panel, active members of the court include Chief Judge Diane P. Wood and Judges Richard A. Posner, Ann Claire Williams, Diane S. Sykes and David F. Hamilton. Judge Joel M. Flaum did not participate in the order.