In a message released ahead of the Eid festival, Mullah Mansour also urged the Taliban to stay united.
His predecessor, Taliban founder Mullah Omar, died in 2013 but his death was only confirmed in July this year.
Mullah Mansour's swift appointment had sparked divisions within the Taliban.
His remarks came as officials said Taliban militants had killed 10 Afghan soldiers after gaining entry to their army post with the help of a collaborator.
The killings, in the northern province of Jawzjan, are the latest in a series of so-called insider-attacks against government forces.
In his message, Mullah Mansour said that "if the country is not under occupation, the problem of the Afghans can be resolved through intra-Afghan understanding".
"If the Kabul administration wants to end the war and establish peace in the country, it is possible through ending the occupation and revoking all military and security treaties with the invaders".
The US and Afghan governments signed an agreement in September 2014 allowing 13,000 foreign troops, most of them from the US, to stay on and support counter-terrorism efforts.
Mullah Mansour also accused the US of attempting to "create an atmosphere of discord and distrust" among fighters and called on Taliban members to "keep your rank and file united in this critical situation".
News of Mullah Omar's death in July disrupted fledgling peace talks between the Afghan government and the Taliban.
Some senior Taliban leaders had been suspicious of Mullah Mansour's support for peace talks hosted by neighbouring Pakistan, and accused pro-Pakistani circles of installing him as the new leader.
Mullah Mansour consolidated his position last week after Mullah Omar's eldest son and brother swore allegiance to him.
However, correspondents say the support of some important Taliban commanders in the south has yet to be secured.
The new leader of the Afghan Taliban, Mullah Akhtar Mansour, has hinted he is open to peace talks with the government if foreign troops are expelled and a security deal with the US is scrapped.