Mugabe and his former opposition foe, Prime Minister Morgan Tsvangirai, formed a power-sharing government in February to end a political stalemate that followed last year's elections.
A new crisis hit the government last week when Tsvangirai and his MDC party said it would stop attending cabinet meetings in protest against the arrest of a senior official and Mugabe's refusal to implement a political pact in full.
In his first public comments on the matter, Mugabe said his party had fulfilled its part of the agreement and he would not to yield to MDC pressure, according to the state-controlled Herald newspaper.
The matters the people are complaining about in the MDC are that we should now voluntarily ... give away aspects of our authority. We will not do that, Mugabe was quoted saying.
They (MDC) can go to any summit, any part of the world to appeal. That will not happen.
Mugabe added that he did not believe the unity government faced collapse.
I do not read that they would want to leave the inclusive government. I think they will come back to it soon.
The Herald said Mugabe and Tsvangirai would resume their weekly meetings on Monday to try to end the impasse.
Tsvangirai, who has been on a regional tour to seek help from leaders who brokered the power-sharing deal, told reporters in Angola on Friday his dispute with Mugabe was a temporary setback that would not lead to the collapse of the pact.
(Reporting by Nelson Banya, editing by Andrew Dobbie)