Mr Corbyn, shadow home secretary Andy Burnham and veteran Labour MP Dennis Skinner were among those attending the demonstration outside Parliament.
Mr Skinner said he wanted the Government to keep its promises.
He said that an inquiry would reveal that “what we suspected at the time is true”.
Mr Skinner added: “The police at Orgreave were called upon to write the same thing over and over again about every single miner they arrested.”
Striking miners and police clashed at Orgreave in 1984 and campaigners want an inquiry into the actions of police, politicians and other key figures.
The conclusion earlier this year of the inquest into the deaths at the Hillsborough disaster and evidence which has subsequently emerged has pointed to connections between the two events.
Sheffield Heeley MP Louise Haigh, who will chair today’s meeting, said recent revelations only made the case for an inquiry “indisputable”.
She said: “Unless we get to the truth about what happened thirty years ago, then the lessons for today will go unlearnt. Our delegation of justice campaigners, human rights barristers, and miners who were there on that day will be pressing the case to the Home Secretary that Orgreave remains an open sore for communities which saw police forces, ostensibly there to serve them, used against them.
“I will be very clear to the Home Secretary that unless we find out the truth, this cloud of past wrongdoing and alleged wrongdoing will continue to hang over police forces across the country.”
Hillsborough campaigner Margaret Aspinall was among those at the rally.
Mr Burnham said the Government could not be “selective” about which injustices were investigated and “which were hidden”.
He told the Press Association: “I pay credit to the Prime Minister for the way she saw the job through on Hillsborough.
“But now, all the evidence points fully towards Orgreave.”
The Orgreave Truth and Justice Campaign (OTJC) wants an investigation into wrongdoing around the police’s handling of events outside Orgreave coking plant, between Sheffield and Rotherham, in June 1984.
A spokesman said they hope Tuesday’s meeting with Amber Rudd will “reinforce the case for a public inquiry into the brutality of the policing of pickets”.
Pickets complained of excessive force by some of the 6,000 officers brought in to police the strike. A total of 95 miners were charged following the clashes but their trial collapsed.
South Yorkshire Police referred itself to the IPCC in 2012 over allegations officers colluded to write court statements.
The watchdog later said the passage of time prevented a formal investigation, but said there was “support” for the allegation that senior police exaggerated pickets’ use of violence.