Emmerson Mnangagwa says he will be a leader for all Zimbabweans in a call for unity after rows broke out over his election victory.
The president appealed for peace and promised an independent investigation into the military after six people were killed in post-election violence.
Opposition leader Nelson Chamisa has described the president's victory as a "coup against [the people's] will".
This was the first election since long-term leader Robert Mugabe was ousted.
Speaking at a press conference, President Mnangagwa said that Mr Chamisa would have "a crucial role to play in Zimbabwe's president and its unfolding future".
He asked the opposition leader to join him in calling for peace and unity in the country, and promised that people's civil liberties would be protected.
Mr Chamisa had earlier called the results "corrupted" and said his MDC Alliance would pursue all legal and constitutional avenues to challenge it.
The opposition leader said he had evidence that ballot boxes were being transported in open trucks allowing them to be tampered with.
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