Musharraf's lawyers Ibrahim Satti and Kamar Afzal went to the apex court to file the appeal but could not complete some formalities before the court closed for the day.
They told the media that they would contend in the appeal that the charge against Musharraf the wrongful confinement of judges during the 2007 emergency was a bailable offence.
The lawyers further said that none of the judges allegedly affected by Musharraf's actions had complained and the FIR was filed by a private individual.
Earlier in the day, the Islamabad High Court revoked Musharraf's bail in a case over the detention of more than 60 judges during the emergency and directed police to arrest him.
However, Musharraf and his security detail sped away from the court before police could act.
Musharraf, 69, was ensconced in his sprawling farmhouse at Chak Shahzad on the outskirts of Islamabad and holding consultations with legal experts.
Ahmad Raza Kasuri, the head of Musharraf's legal team, claimed the former President "went to court under the protection of the state and left with the protection of the state".
Muhammad Amjad, a leader of Musharraf's All Pakistan Muslim League party, said the former President had decided to approach the apex court for relief after consulting his aides."We have decided that since the Supreme Court has already said Musharraf will not be arrested for another case seeking his trial for treason, we will approach the Supreme Court to confirm his bail," Amjad said."It is not necessary that he will be arrested immediately if his bail is rejected suddenly by the High Court Musharraf does not want to resist or disobey an order but he was definitely disappointed (by the High Court's order)," he added.
Sources told PTI that the government was considering a proposal to declare Musharraf's farmhouse a "sub-jail" so that he could be detained there.
Authorities believe it would be better to hold Musharraf at his farmhouse in view of serious threats to his life, the sources said.
Meanwhile, Human Rights Watch said Musharraf's actions in court highlighted his disregard for due legal process.
HRW reiterated its call that Musharraf be held accountable for abuses and said a fair trial for the former military ruler is "key to ending impunity for abuses by Pakistan's security forces".
"Musharraf's act today underscores his disregard for due legal process and indicates his assumption that as a former army chief and military dictator he can evade accountability for abuses," said Ali Dayan Hasan, Pakistan director for HRW."It is essential that Pakistan's military authorities which are protecting the former dictator comply with the Islamabad High Court's orders and ensure that he presents himself for arrest.
Continued military protection for Musharraf will make a mockery of claims that Pakistan's armed forces support the rule of law and bring the military further disrepute that it can ill afford," Hasan said.
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