Sharif's lawyers have petitioned the court to start proceedings against the government for contempt.
Last month, the court ruled that Sharif had an "inalienable right" to return home and that the authorities should not obstruct him.
After the petition was filed, Hamza Sharif, the ex-PM's nephew, told journalists on the steps of the court: "We will fight this battle in the court of law. We are fully confident that we will win, God willing."
He also said supporters would stage street protests, though there was no sign of demonstrations.
"Musharraf is shouting slogans of war against terror in order to win US support"
Ali Abu Hamza, Chichawatni, Pakistan
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Human Rights Watch (HRW), the New York-based organisation, said Sharif must be allowed to return home.
Ali Dayan Hasan, South Asia researcher for HRW, said: "General Musharraf has brazenly flouted international law... violated Pakistan's constitution and defied a direct ruling of Pakistan's supreme court
"Pakistan and Saudi Arabia have colluded in bundling a Pakistani citizen into a plane and forced exile."
Guarded US reaction
The deportation was criticised by the European Union, but the United States, which has valued Musharraf as an ally since the September 11 attacks and rarely presses him on his democratic record, gave a more guarded reaction.
Sean McCormack, US state department spokesman, said the deportation "runs contrary to the supreme court decision", but that it was an "internal matter".
Musharraf's actions could help to undermine the legitimacy of legislative elections due by January 2008.
Ali Ahmed Kurd, a senior member of the Pakistan Bar Council, said lawyers across the country were boycotting courts to protest Sharif's deportation.
Meanwhile, Nawa-I-Waqt, the Urdu-language newspaper, said in an editorial: "The system is based on the crutches of a uniformed president, and the day these crutches are removed the present political system will collapse."
Tariq Azim, Pakistan's deputy information minister, told the BBC that the government had obeyed the court ruling to let Sharif enter the country, but that the former premier chose to go back into exile to avoid facing trial.
Azim said: "It was a choice given to him that either he goes to a detention centre and be detained and tried, or he goes and completes his 10-year [exile] agreement that he has signed with the Saudi government. No hindrance or obstacle was placed upon his entry into Pakistan."
However, Sadiq ul-Farooq of Sharif's Pakistan Muslim League-N party rejected Azim's claim as a "baseless concoction" and said that Sharif had volunteered to be arrested by police at Islamabad airport after he was served a warrant.
Ul-Farooq said: "He [Sharif] said, 'If you have any cases against me, arrest me and send me to jail.' He offered his wrists to them."
He estimated that more than 5,000 Sharif party workers and leaders have been arrested nationwide in recent days, including the party's chairman and Rafiq Tarar, the former Pakistan president.