The US envoy asked Arafat about the incident
The Israelis have accused the authority of trying to smuggle 50 tons of Iranian-made missiles and other weapons into the West Bank and Gaza Strip on board one of its ships.
Israel said its commandos had intercepted the shipment on Friday in the Red Sea, adding that the captain and some of the crew were members of the Palestinian naval police.
Palestinian officials deny the allegations, accusing Israel of trying to sabotage Mr Zinni's attempts to broker a truce between the two sides after 15 months of violence that have left more than 1,000 dead.
Mr Zinni asked Palestinian leader Yasser Arafat about the weapons shipment when the two met on Friday in the West Bank town of Ramallah, US State Department spokesman Richard Boucher said.
The envoy had "expressed our strong condemnation of any attempt to escalate the conflict in the region by militant groups or others," Mr Boucher said.
Israeli Foreign Minister Shimon Peres said Mr Arafat had a choice to make.
"They have to make strategic decision whether they support terrorism or they are against it," he said in a statement.
Mr Peres added that he would be asking the international community to declare Iran - the alleged supplier of the shipment - a supporter of terrorism.
Iran denies that it had any connection with the shipment.
Mr Zinni is trying to move both sides towards accepting a formal truce, the details of which were outlined last year by the head of the US Central Intelligence Agency, George Tenet.
Under this plan, Israel would withdraw its troops from Palestinian areas to positions they held before the outbreak of fighting in September 2000, and the Palestinian security forces would make an all-out effort to prevent attacks on Israelis by Palestinian militants.
Mitchell plan
With a truce in place, the two sides would then implement the proposals of an international commission headed by former US Senator George Mitchell.
Israel would freeze all settlement activity in the West Bank and Gaza, while the Palestinians would dismantle militant groups.
Israeli Prime Minister Ariel Sharon - who also met Mr Zinni on Friday - has said he will only commit himself to the truce deal once there has been a week of complete calm.
There has been a sharp drop in violence since Mr Arafat renewed his commitment to a ceasefire on 16 December, although there has been sporadic violence.