The UN chief, addressing reporters in Bali ahead of a Group of 20 summit, said that talks over the last week had delivered "a lot of progress" on the deal that is set to end on Saturday.
"I am hopeful that the Black Sea grain initiative will be renewed," Guterres said.
"We need urgent action to prevent famine and hunger in a growing number of places around the world," Guterres said.
"The Black Sea grain initiative, and efforts to ensure Russian food and fertilisers can flow to global markets, are essential to global food security."
Russia has said it had yet to decide whether to extend the grain deal beyond November 19, the original date in the agreement.
Moscow has complained that a second agreement brokered by the UN and Turkey on its fertilizers being exempt from sanctions had not been respected.
Ukraine is one of the world's top grain producers, and the Russian invasion had blocked 20 million tons of grain in its ports until the United Nations and Turkey brokered the deal in July.
The renewal of the grain deal is especially important for Africa, which traditionally has imported large quantities of grain from both Ukraine and Russia.