Guterres made the appeal in a report circulated on Monday before the UN Security Council's unanimous approval of a resolution authorising the inspection of vessels on the high seas headed to or from Libya for another year to enforce the arms embargo.
The European Union's Operation Sophia has been the only regional naval operation carrying out inspections.
UN experts monitoring the arms embargo, individual countries, and regional organisations "have all reported on illicit transfers of arms and related materiel into and out of Libya", Guterres noted.
Implementing all measures related to the arms embargo is "of immediate importance in de-escalating the current situation" and is "of critical importance to the protection of civilians and the restoration of security and stability in Libya and the region", the secretary-general said.
'Escalating conflict'
The civil war in Libya in 2011 toppled and later killed longtime dictator Muammar Gaddafi.
The chaos that followed resulted in a divided country, with a UN-recognised but weak administration in the capital Tripoli overseeing the country's west and a rival government in the east aligned with the self-declared Libyan National Army led by renegade military commander Khalifa Haftar.
Each is backed by an array of militias and armed groups fighting over resources and territory.
Haftar launched a military offensive in early April aimed at taking Tripoli despite commitments to move towards elections in the North African country. Clashes receded as the Muslim holy month of Ramadan began in May, but later intensified.
The UK's political coordinator at the UN, Stephen Hickey - whose country sponsored the UN resolution - expressed deep concern after the vote at "the now protracted and escalating conflict", which has led to a deteriorating security and humanitarian situation in Libya.
"Any arms entering Libya will only escalate the conflict and lessen the prospects for a ceasefire," Hickey told the Security Council. "Respecting the arms embargo is only one part of the solution in Libya, which requires a full political dialogue and reconciliation."
Britain, Belgium, France, Germany, South Africa, Ivory Coast and Indonesia reiterated calls for a ceasefire and return to UN-led political talks.
'Constant supply'
South African Ambassador Jerry Matjila said "it is two months since the crisis started in Libya without any respect for this council's calls for a ceasefire by all parties to the conflict", which he said is being "fueled by the constant supply of arms".
While the EU in March extended Operation Sophia's mandate until September 30, it suspended the deployment of ships, saying it would send more planes to monitor the area instead.
Italy commands Operation Sophia, but the populist government in Rome refuses to allow its ships or rescue vessels from aid groups that rescue refugees and migrants to disembark in Italian ports. The EU move on suspending the naval mission was widely viewed as being aimed at easing tensions with Italy's anti-migrant government.
Matjila and Ivory Coast Ambassador Kacou Adom expressed concern at Operation Sophia's suspension of the naval operation. Adom called on countries to immediately make available equipment for the operation "in order to ensure it can be more effective".
Germany's deputy UN ambassador, Juergen Schulz, backed UN calls for all countries to implement the arms embargo, saying in the current environment it is "more important than ever".
"A seemingly unlimited arms supply fuels the erroneous belief in a military solution to the conflict and contributes to the unwillingness of actors on the ground to agree to a ceasefire" and resume the UN-led political process, Schulz said.