While Ukrainian refugees were being handled well, "we have to prepare also for refugees coming from other areas because of the food security," the interim executive director of the EU's Frontex agency, Aija Kalnaja said.
Kalnaja was speaking as she arrived in Prague for a meeting of EU interior ministers that had been expanded to also include the ministers from non-EU countries Ukraine and Moldova.
This, as the head of UNHCR, Filippo Grandi, warned in June that unless the growing food crisis caused by Russia was quickly resolved, the number of displaced people globally would swell well beyond the record 100 million already counted.
Russia's war, which started February 24, has already provoked the biggest refugee outflow since World War II, prompting the EU to offer fleeing Ukrainians temporary protection.
According to the UN, the 27-nation European Union is hosting 5.6 million Ukrainian refugees.
Poland has the biggest number, 1.2 million, while the Czech Republic has 400,000, the largest proportion on a per capita basis.
The grain shortage caused by the Russian attack upon Ukraine has raised food prices that have particularly hit Africa, where various agencies including the UN have warned of growing starvation.
And hunger has sent waves of Sub-Saharan Africans to the continent's Mediterranean coast, where they risk their lives in small boats trying to reach the European Union's southernmost island outposts, or to Spain across the Straits of Gibraltar.