Mansour appealed for unity among his fighters following the death of the group’s previous leader, Mullah Omar, in a 30-minute audio recording released to journalists.
Some factions within the group have reportedly opposed Mansour’s appointment, including one which wanted Omar’s son to succeed him.
A Taliban spokesman confirmed Omar’s death on 30 July, although it is unclear when or where he died, with some reports suggesting the former chief had been deceased for more than two years.
“We should keep our unity, we must be united, our enemy will be happy in our separation,” Mansour was quoted as saying in the message by the Associated Press news agency.
“This is a big responsibility for us. This is not the work of one, two or three people. This is all our responsibility to carry on jihad until we establish the Islamic state.”
He continued: “We have to continue our jihad, we shouldn’t be suspicious of each other. We should accept each other.
“Whatever happens we must comply with Sharia law, whether that be jihad, or talks, or an invitation to either.”
But a Taliban spokesman told the BBC that Mansour’s appointment was made without the consultation of certain factions within the jihadist group.
“According to Islamic rule and principles, when a leader dies, a Shura (council) is called, then its leader is appointed,” he said.
The spokesman added that the council would soon hold a meeting to select a new leader.
Analysts say the Afghan Taliban may splinter in the wake of Omar’s death amid growing defections of the group’s fighters to Islamic State (Isis), which has established a small franchise in the country.