"The Secretary-General expresses his solidarity with the people and the Government of the United Kingdom as they fight terrorism and violent extremism," said a statement by a UN spokesperson, which denounced the deadly incidents.
He also expressed Guterres' condolences to the families of the victims and wished the injured for a swift recovery.
Seven people were killed and dozens more injured when a van sped across London Bridge on June 3, ramming numerous pedestrians.
After the van came to a halt, the attackers stabbed several people in the capital's Borough Market, a crowded weekend gathering spot. The three assailants were later shot by the police.
"This is a struggle in many parts of the globe that compels the international community to join up efforts to bring to justice those who use such inhuman tactics while also protecting and promoting the fundamental values, rights and principles that terrorists so fervently seek to undermine," the statement concluded.
Police in London named two of the three suspects in the van and knife attack near London Bridge. They identified 27- year-old Khuram Shazad Butt, a British citizen born in Pakistan and Rachid Redouane who had claimed both Libyan and Moroccan nationality.