Mujuru died on Tuesday after his farm house in Beatrice was gutted by fire, sparking speculation that he was murdered.
Mugabe deviated from his speech to give counsel to his supporters who constantly booed Prime Minister Morgan Tsvangirai and deputy prime ministers Arthur Mutambara and Thokozani Khupe.
He said there was no need to fight as Zimbabweans were one.
“Lets create peace. We are very happy that over the past few months there have been remarkable peace,” he said.
Mugabe said people must be free to choose leaders of their choice during elections.
Mugabe said Mujuru was a unifier as he was instrumental in forging a united defence force soon after independence.
“He sought to bring about a difference, a change of fortune and fate in the lives of black Zimbabweans for too long occupied, for too long oppressed, suppressed and sidelined in the affairs of their country,” he said.
He said Mujuru was a symbol of the struggle, a figure of rich memories and inspiration.
The veteran ruler described Mujuru as a legend who had managed to capture the respect and collective grief of the whole nation
Mugabe also refrained from reading his prepared speech that appeared more combative with the Zanu PF sanctions mantra dominating.
Part of the prepared speech read: “Above all, Rex shunned sanctions as a form of assault on the people of Zimababwe.
“He was with us when we organised the anti-sanctions campaign. He signed the petition.
“He denounced those sanctions and those behind them. How do you shed genuine tears for Rex when you stand opposed to the very ideals for which he fought and struggled?
“How do you claim him and his legacy when you stand against his cause and the cause of the very people whose grievances motivated him?
“How do you claim him today when you traffic with those he traded bullets with only yesterday?”
Meanwhile, an estimated record crowd of 50 000 was at the national shrine.
For the first time in many years Zanu PF did not have to bus people to attend the burial as was the norm when they bury other heroes at the shrine.
Zimbabweans from all walks of life and political affiliation came in their thousands to bid farewell to the late general.
Some people were perched in trees to enable them to follow proceedings while cars had to be parked at the National Sports Stadium and along Bulawayo road.
People had to walk almost 2 km to the national shrine.
Among those that attended were opposition leaders Dumiso Dabengwa, Tsvangirai, Khupe, Speaker of Parliament Lovemore Moyo, Welshman Ncube and Arthur Mutambara.
Cabinet ministers from the three governing parties also attended.