Griffiths said Turkish, Russian and Ukrainian military officials were working with a UN team at a Joint Coordination Centre in Istanbul to hammer out standard operating procedures for the deal agreed by the four parties last Friday.
"That is a detailed negotiation based on the agreement," Griffiths told UN member states in a briefing on Thursday.
"But without those standard operating procedures we cannot manage a safe passage of vessels."
He acknowledged that "the devil was in the details".
Shipping companies and the insurers that cover vessels need to be assured that the journey is secure with no threat of mines or attacks to both the ships and their crews.
These are typically covered in accepted maritime practices known as standard operating procedure.
"It's not just a matter of whether there is a ship, or two, or three available in the ports ready to move out. They need to move safely and that means that we have to be clear where exactly the channel is," Griffiths said.
Russia and Ukraine are major global wheat suppliers and the Russian invasion on February 24 of its neighbour sent food prices soaring, stoking a global food crisis the World Food Programme says has pushed 47 million people into "acute hunger".
The agreement aims to allow safe passage for grain shipments in and out of Ukrainian ports, blockaded by Russia since its invasion.
Russia has blamed Ukraine for stalling shipments by mining the port waters.
"We are hopeful of course, planning, but hopeful for the first ship movements to take place within days - hopefully tomorrow - out of those ports," Griffiths said.
"There are vessels of course in those ports with grain on board ready to move, and they will be the first to move, and then we will start having ships going in - inspected and going in."
He said the head UN official at the Joint Coordination Centre, Frederick J Kenney from the International Maritime Organisation, had a meeting with insurers and shipping companies on Wednesday.
"I'm told that it was very encouraging set of conversations," Griffiths said.
"We'd kept them informed as we went through the negotiations... We have to see this move."
"It is commercially viable," he said, adding that the UN World Food Programme is "actively looking" at buying Ukraine grain.
Ships going in to collect grain will be inspected at a Turkish port "to ensure there's no contraband, no weaponry going in on these vessels," Griffiths said.
"Inspections are likely to occur at anchorage north of the Bosphorus, details to be confirmed," said Ismini Palla, UN spokesperson at the Joint Coordination Centre.
UN and Turkish monitors in Ukraine's Odesa port will then make sure that grain is loaded on to the ships, which will then leave "in the system of monitoring which we will establish" out of the Black Sea and into the world, Griffiths said.
He said they knew from early on in negotiations that de-mining the approaches to Ukrainian ports was not going to work because it would take too long - UN mine officials had estimated it would take at least four months to do it properly.
