"The lawyers' struggle has entered into a decisive phase," said Munir Malik, a leader of the lawyers' movement.
"We are heartened by the support from the civil society and political parties," he told local television.
Chaudhry, who was given a rousing welcome by a large crowd on his arrival in Lahore overnight, addressed demonstrators on Thursday morning, telling them: "If there's an independent judiciary, the democratic system will work.
"You people have started a revolution which has to reach its logical conclusion," Chaudhry told a crowd of hundreds in the city of Lahore, the half-way point of the rally.
The caravan will pass through different towns during its 270km journey to Islamabad, where it is expected late on Thursday night or early on Friday, lawyers' spokesman Azhar Siddique said.
Political parties have set up camps in Lahore and Islamabad for the marchers.
"We will stage a sit-in outside the parliament for an indefinite period," Amin Javed, secretary of the Supreme Court Bar Association, said.
"The protest will be peaceful. Nobody will be allowed to create any unpleasant situation," he added.
Sharif, who was removed from power by Musharraf in a 1999 coup, described the campaign as a struggle for the survival of the country.
He has supported calls for the restoration of the judges whom Musharraf sacked during a state of emergency on November 3 when it appeared they would overturn his re-election as president the previous month.
Sharif's Pakistan Muslim League-N party quit the cabinet last month to protest against the coalition's failure to honour a May 12 deadline for their restoration.
The biggest party in the coalition, the Pakistan People's Party of the assassinated former premier Benazir Bhutto, is drawing up a package of constitutional reforms that is set to include the reinstatement of the judiciary.
But it has been hampered by disagreements over whether to limit the judges' power and whether the coalition will directly confront Musharraf.