These calls by António Guterres were accepted and claimed by the Afghan official at the United Nations during a Security Council meeting, AFP news agency reports.
"We urge the Taliban to seize this moment and win the trust and goodwill of the international community by recognising - and defending - the fundamental human rights that belong to all girls and women," the Portuguese diplomat stressed.
The UN official expressed "deep concern" over recent reports of arbitrary arrests and abductions of activists, calling "vigorously" for their release.
Naseer Ahmad Faiq, the current UN official in Afghanistan since the departure in mid-December of a diplomat sacked by the Taliban, spoke at the end of the meeting, assuring to speak "on behalf of the Afghan people" and not of the former government overthrown in August.
"I ask the Taliban to put an end to the human rights violations" reported by NGOs, to "allow women to work" and to "open the doors of schools and universities to girls", he shot back.
The diplomat also called on the Taliban to provide information on the whereabouts of activists who have recently disappeared and for them to be "released immediately".
Ahmad Faiq also asked the Security Council to convene an "international conference to discuss intra-Afghan issues" with the aim of achieving "the formation of an inclusive and accountable government, reforming the constitution and allowing Afghans to choose their leaders through elections".
The UN secretary-general had earlier urged the "international community to strengthen its support for the Afghan people", in particular through the release of funds frozen in Washington by the World Bank and the United States, at a time when the Middle Eastern country is "on a knife edge".
"More than half of Afghans face extreme levels of hunger" and "some families are selling their babies to buy food", the Portuguese warned.
Also the Chinese ambassador to the UN, Zhang Jun, commented on this extreme situation, revealing that one woman "sold her two daughters and a kidney" to be able to feed her family.
"It is a human tragedy," he denounced, implicitly calling on the United States to lift "unilateral sanctions" and allow Afghanistan access to funds.
The US has blocked nearly $9.5 billion (€8.3 billion) in reserves from the Afghan Central Bank, equivalent to half of the country's gross domestic product (GDP) in 2020.
The International Monetary Fund (IMF) and the World Bank have also halted their activities in Afghanistan, suspending aid and €300 million in new reserves issued by the IMF in August.
António Guterres argued that the Afghan economy must be "revived" with more money.
"Without action, lives will be lost and desperation and extremism will increase," while a "collapse of the Afghan economy could lead to a mass exodus of people fleeing the country," he warned.
Afghanistan faces a severe economic crisis, affected by food shortages and growing poverty, intensified with the Taliban coming to power in August.
The Middle Eastern country also faces a severe cash crunch after international donors suspended aid that had supported the government budget for 20 years.