The senior politician was speaking about the situation in the Ardoyne area of the city at the opening session of his party's annual conference.
"There must be a solution," Mr Dodds said on Friday.
"The solution comes through dialogue and it comes through common sense.
"We can't have a situation on our streets where people are feeling that there is no fairness, no justice in terms of their rights and about shared space."
A determination by the Parades Commission meant that the Twelfth return parade could not use the same route in the afternoon as it had for its outward morning journey, resulting in a stand-off.
A long-running protest camp has been established at Twaddell Avenue over the issue.
Mr Dodds added that people should be allowed to protest, as long as it was "respectful".
"It can't be about the denial of human rights, which is what's going on at the minute at Twaddell," he said.