The UN and Turkey brokered the agreement last month after warnings that the halt in grain shipments caused by Russia's invasion of Ukraine could lead to severe food shortages and even outbreaks of famine in parts of the world.
Ukrainian Infrastructure Minister Oleksandr Kubrakov said there were plans to step up shipments.
“We are gradually moving on to larger volumes of work. We plan to ensure the ability of the ports to handle at least 100 vessels per month in the near future,” he said.
Ukraine is also expected to soon start exporting grain from its Black Sea port of Pivdennyi, an expansion that would allow it to send out at least three million tonnes of goods a month, Mr Kubrakov said on Facebook.
Before Moscow began what it calls its “special military operation”, Russia and Ukraine together accounted for about a third of global wheat exports.
In peacetime, Ukraine exported up to six million tonnes of grain from its Black and Azov ports every month.
The resumption of grain exports is being overseen by a joint co-ordination centre in Istanbul where Russian, Ukrainian, Turkish and UN personnel are working.
The first cargo ship left Ukraine under the terms of the agreement on Monday last week, and another three followed on Friday.
The co-ordination centre said late on Saturday that it had authorised five new vessels to pass through the Black Sea corridor — four outbound from Ukraine's Chornomorsk and Odesa ports, carrying 161,084 metric tonnes of foodstuffs, and one inbound to pick up grain.
The ships that left Ukrainian ports included Glory, with a cargo of 66,000 tonnes of maize bound for Istanbul, and Riva Wind, loaded with 44,000 tonnes of maize, heading for Turkey's Iskenderun.
Turkish defence ministry said the other two vessels that left Ukraine were China-bound Star Helena, with a cargo of 45,000 tonnes of meal, and Italy-bound Mustafa Necati, carrying 6,000 tonnes of sunflower oil.
Later on Sunday, Ukraine's Infrastructure Ministry said the bulk carrier Fulmar S, which had reached the port of Chornomorsk on Saturday — the first foreign-flagged ship to arrive in Ukraine since the conflict — was ready for loading.
The joint co-ordination centre said it had nearly finished drafting procedures to enforce the grain deal and they would be published in days.
It also said it had authorised the movement, pending inspection, of Osprey S, inbound for Chornomorsk. That ship is currently anchored north-west of Istanbul.
The Turkish Defence Ministry said the joint co-ordination centre had completed inspections of Rojen, carrying 13,000 tonnes of maize to Britain, as well as Polarnet, which is taking 12,000 tonnes of maize to a Turkish port, and Osprey S, which is heading to Ukraine.
On Saturday, the co-ordination centre completed its inspection of Navistar, one of three vessels that left Ukrainian ports on Friday.
The first ship to leave a Ukrainian port under the deal will not arrive in Lebanon on Sunday as planned, the Ukrainian embassy in Lebanon said. The Razoni left Odesa on Monday carrying 26,527 tonnes of maize.
The embassy told Reuters the ship was “having a delay” and “not arriving today”, with no details on a new arrival date or the cause of the delay. Refinitiv Eikon data showed the Razoni off the Turkish coast on Sunday morning.