The United Nations on Sunday awaited a response from Russia on renewing a deal that allows Ukraine to export its grain amid a wartime blockade, a necessity in helping keep global food prices stable.

The Black Sea Grain Initiative, brokered by the United Nations and Turkey, is a rare example of fruitful negotiations between Ukraine and Russia since the start of the full-scale invasion. The deal was initially reached a year ago, allowing Ukraine to restart the export of millions of tons of grain that had languished for months.

But Russia has repeatedly threatened to pull out of the deal, which has been renewed only for short periods. The last day of the latest extension is Monday.

In a bid to answer one of Russia’s key demands before this latest deadline, the United Nations secretary general, António Guterres, sent a letter to President Vladimir V. Putin of Russia last week with proposals that would “remove hurdles affecting financial transactions” through Russia’s agricultural bank “and simultaneously allow for the continued flow of Ukrainian grain through the Black Sea,” according to a U.N. statement.

Two days later, Mr. Putin called the deal a “one-sided game,” again threatening to pull out of it because of what he considered unmet conditions, Tass, Russia’s state news agency, reported. “We may suspend our participation in this agreement. And if everyone reiterates that all promises given to us will be fulfilled — let them fulfill these promises. And we will immediately join this agreement. Again,” he said, according to Tass.

One cargo ship departed the Ukrainian port of Odesa on Sunday, bound for the Netherlands. The last shipment before that had been Thursday.

Jake Sullivan, the U.S. national security adviser, said Sunday in an interview with CBS’s “Face the Nation” that it wasn’t clear what Mr. Putin would decide.

“We are prepared for any scenario, and we’re working closely with the Ukrainians on that,” he said.

The invasion prompted the United States and European countries to tighten sanctions on Russia, effectively turning it into a pariah state. Some analysts have argued that Moscow is trying to use the grain deal as leverage to soften these sanctions.

Russia has complained that while the agreement has allowed Ukraine’s food exports to reach markets, the Western sanctions have restricted the sale of Russia’s agricultural products, and it has demanded that steps be taken to facilitate its own exports of grain and fertilizers. The Kremlin’s other demands included restoring an ammonia pipeline that crosses Ukraine to facilitate exports, but Ukraine has refused to grant consent.

The deal was first brokered to alleviate a global food crisis exacerbated when Russia effectively blockaded Ukrainian ports at the start of its invasion. Ukraine is a major exporter of grain and other food crops, and global wheat prices soared. Although Ukraine’s allies began accepting more shipments over land, there was little choice but to strike a deal with Russia to ease the crisis and allow Ukrainian farmers to continue producing.

Since the Black Sea Grain Initiative began, Ukraine has used it to export 32.8 million tons of grain and other foodstuffs, according to U.N. data, and the agreement has prevented hunger crises from worsening in some countries in the Middle East and Africa.

Under the deal, Ukrainian corn and wheat are the leading exports, with 90 percent of corn and 60 percent of wheat shipped to high- or middle-income countries. The volumes shipped to low-income countries are roughly the same as before the invasion, according to U.N. data.

But the volume of grain exported from the Ukrainian ports in the Black Sea has been slowing in recent weeks, according to U.N. data. The same thing happened weeks before the deal’s previous expiration date, in May.

Under the terms of the deal, Ukraine’s ships have been given safe passage to the port in Istanbul, where inspectors have checked them. Empty ships have also been checked in Istanbul en route to Ukraine’s ports to verify that they are not carrying weapons or other goods banned under the agreement.

Here’s what else is happening in the war:

• Speaking to Russian state TV, Mr. Putin said in clips released on Sunday that Ukraine’s monthlong counteroffensive — which has so far captured a few miles of territory — “has not had success,” and that Russian forces were holding out throughout the front line. Mr. Putin added that Russia was even staging its own attacks in some areas. On Sunday afternoon, a Ukrainian deputy defense minister, Hanna Malyar, said in a Telegram post that Russian forces have been conducting offensive operations near Kupiansk, a city in the Kharkiv region, and in parts of the Donetsk region.

• In the clips from the state TV interview, which airs on Sunday evening in Russia, Mr. Putin also said that the recent decision by the United States to send cluster munitions to Ukraine showed the scale of ammunition shortages facing Kyiv, adding that Russia may retaliate if these weapons are deployed on the battlefield. Mr. Putin falsely claimed that Russia had not used cluster munitions in Ukraine despite dozens of cases documented by the United Nations, mostly in the early months of the war.

  The Russian president’s comments, which were released by the Kremlin on Sunday, raise the prospect of much wider deployment of cluster munitions in the conflict, which would threaten to cover the area of the fighting with unexploded ordnance for years, posing a significant risk to civilians.

• Britain’s defense secretary, Ben Wallace, told The Sunday Times of London that he would resign from his post, probably in the coming months, after four years in the role. Britain has been one of Ukraine’s staunchest allies since Russia’s full-scale invasion began. Mr. Wallace said last week that Ukraine should show more gratitude for Britain’s military support, adding, “We’re not Amazon,” comments that Prime Minister Rishi Sunak distanced himself from.