Turkey helped broker the accord and said immediately after the double cruise missile hits that it had received assurances from Moscow that Russian forces were not responsible.
But Russia's defence ministry rolled back on the denial Sunday, saying the strikes had destroyed a Ukrainian military vessel and arms delivered by Washington.
"High-precision, long-range missiles launched from the sea destroyed a docked Ukrainian warship and a stockpile of anti-ship missiles delivered by the United States to the Kyiv regime," it said.
"A Ukrainian army repair and upgrade plant has also been put out of order."
The strikes have cast a shadow over the milestone accord -- that was hammered out over months of negotiations and signed in Istanbul -- to relieve a global food crisis.
'Order of peace'
United Nations chief Antonio Guterres, who presided over the signing ceremony Friday, "unequivocally" condemned the attack. The United States meanwhile said it "casts serious doubt" over Russia's commitment to the deal.
Western nations repeated their condemnation of Russia's military assault on Ukraine after the strikes.
German president Frank-Walter Steinmeier called the invasion a war against the unity of Europe.
"We must not let ourselves be divided, we must not let the great work of a united Europe that we have begun so promisingly be destroyed," he said in a speech Sunday.
Cereal prices in Africa -- the world's poorest continent where food supplies are critically tight -- surged because of an exports slump.
Lavrov, who will visit Uganda, Ethiopia and Congo-Brazzaville on the tour, told his Egyptian counterpart Sameh Shoukry that Russia would meet grain orders.
"We confirmed the commitment of Russian exporters of cereal products to meet their orders in full," he said in a press conference.
Zelensky said the strikes on Odessa showed Moscow could not be trusted to keep its promises.
Under the deal brokered by Turkish President Recep Tayyip Erdogan and Guterres, Odessa is one of three designated export hubs.
Ukrainian officials said grain was being stored in the port at the time of the strike, but food stocks did not appear to have been hit.
There was no response from Moscow until Sunday, but Turkish Defence Minister Hulusi Akar said before that Russia had denied carrying out the attack.
Kherson 'liberated' by September
Huge quantities of wheat and other grain have been blocked in Ukrainian ports by Russian warships and the mines Kyiv laid to avert a feared amphibious assault.
Zelensky has said around 20 million tonnes of produce from last year's harvest and the current crop would be exported under the agreement, estimating the value of Ukraine's grain stocks at around $10 billion.
Diplomats expect grain to only start fully flowing by mid-August.
The agreement in Istanbul has brought little reprieve on the battlefield where Russian forces were carrying out bombardments across the sprawling front line over the weekend, Ukraine's presidency said Sunday.
It said among attacks in the industrial east and south, four Russian cruise missiles Saturday had hit residential areas in the southern city of Mykolaiv, injuring five people, including a teenager.
In a devastated village near Ukraine's southern front line Stanislav, a 49-year-old who joined Ukraine's armed forces after Russia's invasion, said many people were afraid.
"But what can we do, we need to defend our homeland, because if I don't do it then my children will be forced to do it," he said.
An official in the nearby Kherson region in the south said a Ukrainian counter-offensive for the territory Russia captured early in the invasion would be over by September.
"We can say that a turning point has occurred on the battlefield. We are switching from defensive to counteroffensive actions," Sergiy Khlan, an aide to the head of Kherson region, said in an interview with Ukrainian television.