A German home-schooling family seeking asylum in the United States faces deportation after the U.S. Supreme Court said Monday it would not hear their case.

The justices rejected an appeal from Uwe and Hannelore Romeike, who claim the German government is persecuting them because they want to raise their children in accordance with their Christian beliefs.

The family moved to Morristown, Tenn., in 2008 after facing fines and threats for refusing to send their kids to a state-approved school in Germany, which is required by law in that country. If the Romeikes had stayed in Germany, they risked losing custody of their children.

Initially, the family was granted asylum in 2010 based on religious freedom grounds, but the Obama administration decided to appeal that decision.

"While this is the end of the line for normal legal appeals, we are not giving up," Michael Farris, chairman of the Home School Legal Defense Association and lead counsel for the Romeikes, said in a written statement.

The family argues that German laws violate international human rights standards. But the U.S. 6th Circuit Court of Appeals rejected that claim and ruled that U.S. law does not grant asylum to every victim of unfair treatment.

According to Germany's highest court, the country's ban on home-schools was created to make sure that religious home-schoolers do not become a "parallel society."

The family's last hope was to plead their case to the Supreme Court -- but Monday's decision by the justices not to hear the appeal, almost assuredly means the family must now return to Germany.

"We will pursue changes to the asylum law in this country to ensure that religious freedom is once again vigorously protected in our policy," Farris said. "I am just glad that the Pilgrims did not face this anti-religious policy when they landed in Plymouth Rock. After all, the Pilgrims left England to find religious freedom, but they left Holland to find a place that was both safe for their children and which provided religious freedom."

The Associated Press contributed to this report.