Fayyad is "the right person for the right job at the right moment," Guterres said at the 5th World Government Summit.
Last Saturday, US ambassador to the UN, Nikki Haley, blocked the appointment of Fayyad, saying Washington was "disappointed to see a letter indicating the intention to appoint the former Palestinian Authority Prime Minister to lead the UN Mission in Libya."
The US is a veto-wielding permanent member of the UN Security Council.
"For too long the UN has been unfairly biased in favor of the Palestinian Authority to the detriment of our allies in Israel," Haley said.
Fayyad, 64, served as prime minister of the Palestinian National Authority in 2007-2013. He had also served as a finance minister.
Fayyad was appointed to replace the German diplomat, Martin Kobler, who has been serving as the UN special envoy to Libya and the head of the UN Support Mission in Libya since November 2015.
Guterres said Fayyad is the "right person... recognized everywhere."
"He has the competence. Objecting the envoy is a loss for Libya, the Libyan people," the UN chief said, adding that containing the conflict in Libya is "in everybody's interest."
Guterres became UN secretary-general on Jan. 1, arrived here on Monday after visiting Turkey and Saudi Arabia, the first two stops of his Middle East tour, which will also take him to Oman, Qatar, and Egypt.
XINHUA/MNA