The main opposition Bangladesh Nationalist Party (BNP) and its 19 allies staged the rally as they launched a string of fresh protests aimed at forcing early elections.
The protests come just months after the ruling Awami League party won parliamentary elections that were boycotted by the opposition.
Between 20,000 and 25,000 people, defying driving monsoon rains, attended the rally in the capital's historic Suhrawardy Uddyan garden, police inspector Sirajul Islam told AFP.
Senior opposition leader Fakhrul Islam Alamgir said the new broadcast policy was "anti-people", "anti-democracy" and aimed at allowing the government to stay in power forever.
"Mass media comes under attack whenever Awami League comes to power," Alamgir said, charging that the broadcast policy was designed to silence dissent and conceal government misdeeds.
The government approved the new policy early this month following a string of media reports alleging government corruption.
The Bangladesh chapter of anti-graft group Transparency International has said the policy clashes with the country's constitution as it bans the broadcast of any programme that undermines or ridicules the armed forces, law enforcement agencies or officers.
"The policy conflicts with the country's constitution, democratic norms and values, human rights and Right to Information Act," its chief, Sultana Kamal, said last week.
The government has rejected charges that the policy goes against the constitution.
Tuesday's rally was the first major protest by BNP-led opposition parties since they boycotted the January 5 polls, alleging they would be rigged. The opposition has vowed a surge in action aimed at forcing fresh elections.
The boycott resulted in an easy victory for the Awami League and its allies, which won all the seats.