The country has in recent years seen an upsurge in violence and an increase in civilian casualties, Efe news reported.
"We want to have relations with the world and answer their questions and mitigate their concerns so that we will protect our country from being harmed by others in the future, and others will also not be harmed by our country," he said.
Akhundzada said the group "has been continuing to make diplomatic efforts aimed at resolving the issue".
"We have nominated the political office for this purpose as well as for maintenance of relations with the world and pertinent entities (for peaceful and diplomatic efforts)," he said.
The Taliban has a political group in Qatar that has in the past made attempts to hold peace talks.
However, after being appointed the Taliban's leader in May, Haibatullah said he would follow in the footsteps of his predecessor Mullah Akhtar Mansour and not join any peace talks with the Afghan government.
"Now that we have control over many areas of the country, it is time for us to reap the fruit of the 15-year-long jihad" since the US-led invasion toppled the Taliban regime in 2001, said the leader in his message.
According to US sources, the Taliban currently controls around one third of the country, amid increasing violence and civilian deaths since the NATO military mission ended on January 1 last year.
On Wednesday, the UN appealed to the international community to step up aid to Afghanistan.
