"People, your friends are committed not to betray you on the path of fighting liars and fraudsters," he said in a statement carried on his official website, Kaleme.com.
"With respect to this commitment, the only way that I recommend is to continue on the green path that you have followed in the past months … with small and large gatherings, campaigns and questions," Mousavi said.
His call came two days after Iran's conservative-dominated parliament united behind President Mahmoud Ahmadinejad to approve the vast majority of his new cabinet, reportedly after supreme leader Ayatollah Ali Khamenei intervened.
Mousavi — who came second in the June 12 poll — dismissed hardliner Ahmadinejad's re-election as a "shameful fraud" as hundreds of thousands of Iranians poured on to streets in protest.
Dozens of people were killed and thousands arrested in the protests, which plunged Iran into its worst internal political crisis since the 1979 Islamic revolution.
Khamenei has strongly backed Ahmadinejad, dismissed allegations of fraud, and pointed an accusing finger at the West over the post-election unrest, as well as blaming opposition leaders for the ensuing violence.
The public protests have died down over the past month in the face of a heavy crackdown by police and Islamic militiamen, but the election and its aftermath have bitterly divided the country's political elite.
The authorities have faced mounting criticism over their handling of the protests amid charges that protesters were raped and tortured in custody.
The detained former spokesman for reformist former president Mohammad Khatami, Abdollah Ramezanzadeh, claimed on Saturday he had been severely beaten as he was being arrested, as had his son.
Ramazanzadeh, who said he was being held in solitary confinement, told the reformist parlemennews webiste his arrest "was only to settle political scores" and that he was being pressured to make a public confession.
Hundreds of people are still in prison, and 140 people — including senior reformists and journalists — have been put on trial on charges of seeking a "soft" overthrow of the regime and inciting protests.
Ahmadinejad himself has called for opposition leaders to be prosecuted over the unrest, while the opposition describes the hearings as "show trials."
Mousavi had previously said he would continue to protest via a social movement named the "Green Path of Hope."
"In the green movement we do not want anything unconventional and unexpected, but we do want to restore people's lost rights, those enshrined in the constitution," his website said.
"We want a revival of the forgotten goals of the revolution, freedom of speech, freedom after expression and freedom of choice."
Mousavi urged opposition supporters to strengthen their "social cells" and extend links within "family and neighbours' meetings, school reunions, work-out groups, religious congregations, cultural and professional associations."
He said such networks could be used to pass information "faster and more effectively than through any mass media."
Mousavi repeated his demand for the release of all detainees and a "fact-finding group to investigate the fraud and punish offenders."
The moderate former premier also called for "preventing military men from interfering in politics and financial activities."
Iran's elite Revolutionary Guards Corps accused the opposition of seeking to undermine the Islamic regime in the post-election protests and vowed to crack down on efforts to stage a "velvet revolution."
The guards and their affiliate Basij militia played a crucial role in suppressing the demonstrations, and several from among their ranks were later offered cabinet posts by Ahmadinejad.
