PSNI Chief Constable George Hamilton said he feels he is in "an impossible position" over legacy issues.
Representatives from the police, loyalism and republicanism debated legacy at west Belfast festival Féile an Phobail.
Dealing with the legacy of the Troubles is one of the most controversial issues in Northern Ireland.
"As a police officer, as a chief constable, as a human being, I want the truth to emerge," said Mr Hamilton.
The British government is conducting a consultation process, asking the public for their views on legacy issues in Northern Ireland.
Mr Hamilton faced criticism from some members of the audience, who accused him of withholding information from families of victims.
"I feel like I'm in an impossible position, caught between legal obligations, on one hand, financial constraints on the other and, if I had a third hand, it would be about public expectations," he said.
Loyalists and republican representatives both said their views must be taken into consideration.
"Loyalists have not had a voice at the table however you judge it," said Winston Irvine, a loyalist representative.
"I don't think we have an option not to deal with this issue.
"The consequence of not dealing with this issue means that we will keep the burden and the poison that we have all had to experience, live with and grapple through on the next generation."
The panel all agreed that legacy issues must be dealt with as a matter of urgency.
"You can't bury this issue - it's not going to go away, it'll re-emerge on down the years," said Sean Murray, a republican activist.
"We need to develop mechanisms which most people can buy into. I don't think we'll ever get to a stage where everyone will buy into it."