The secretary-general said he was also concerned about "peace in the home."
"Across the globe, as the pandemic spreads, we are also witnessing an alarming increase in violence against women and girls," he pointed out.
Guterres said he had launched an appeal to mobilize better protection for women and asked religious leaders "to unequivocally condemn all acts of violence against women and girls and to uphold the bedrock principles of equality."
The coronavirus pandemic is also exposing inequalities everywhere, he underlined, including economic disparity and unequal access to health care.
"Poverty could rise by 500 million people -- the first increase in three decades," he stated, adding that this is why he is advocating for a global relief package amounting to at least 10% of the global economy.
Guterres also said that it is important that any COVID-19 treatments found or developed -- including a vaccine -- be safe and available to everyone.
"In an interconnected world, none of us is safe until all of us are safe," he said. "This vaccine needs to be the people's vaccine."
In the interview, the secretary general also said religious leaders have a "crucial role to play" during the pandemic in promoting mutual respect within their communities.
"They are well-positioned to challenge inaccurate and harmful messages, and encourage all communities to promote non-violence and reject xenophobia, racism and all forms of intolerance," he said.
Religious leaders can leverage their networks "to support governments in promoting public health measures recommended by the World Health Organization," he said, and "to dispel false information and rumors."