The SDLP leader Claire Hanna called for “political leadership” and said it was “necessary to de-escalate”.
Hanna, who was at the protest, has called on the chief constable and Northern Ireland secretary to “use every power available” to intervene, and said she had reminded both that they had the “ability to revoke any permission for this parade”.
Following talks at Hillsborough, her party called for an international mediator to help resolve the dispute, with Sir Chris saying he is “giving consideration to anything that anybody comes up with”.
He said he is determined to keep on working and talking with people, but added that “we haven’t got a solution yet”.
Also speaking after the meeting, UUP leader Jon Burrows said the rule of law needed to apply to “everyone”, and that Stormont has been “put under threat”.
“It is vital that everyone obeys the law. I don’t care who that is. I don’t care how senior you are. The law applies to everyone. It cannot be enforced basically on the basis of it might be politically inconvenient,” he added.