The talks came as the health ministry in Hamas-run Gaza said relentless Israeli bombing has killed more than 9,700 people in the Palestinian territory, mostly women and children.
Israel has said it will destroy Hamas after the Islamist group's October 7 attacks that officials in the Middle Eastern nation say killed 1,400 people, mostly civilians.
Supplies of water, electricity, fuel and food were cut off to the impoverished and densely populated territory in the aftermath of the Hamas attacks.
Blinken and Christodoulides discussed the situation in the Middle East, government spokesman Konstantinos Letymbiotis said in a post on X, formerly Twitter.
Their conversation at Larnaca airport included "a dedicated, one-way maritime corridor of sustained flow of humanitarian aid from Cyprus to civilians in Gaza", Letymbiotis said.
Earlier Sunday, Christodoulides said France, the European Commission and Israel backed Nicosia's initiative to open a humanitarian sea route.
"On that basis, we are talking with the United Nations because the UN will receive the aid and not Hamas so that it reaches the population," Christodoulides told reporters.
After raising the plan with European Union leaders last month, Christodoulides said he had spoken to Israeli Prime Minister Benjamin Netanyahu and French President Emmanuel Macron about the issue.
"The Republic of Cyprus is trying, within its capabilities, to ensure that humanitarian aid to Gaza is uninterrupted," said Christodoulides.
He said Cyprus was taking the initiative as the nearest EU member state to the region — the island is about 370 kilometers from Gaza — and because of its good relations with Arab states and Israel.
"It is important that both the French president and the president of the (European) Commission have endorsed our initiative. We are working on the details so that it can be implemented," Christodoulides said.
He said, "we must be ready at any moment, and as soon as conditions allow it, to proceed with implementing this proposal."
Asked whether there were discussions with Israel on a cease-fire to provide humanitarian aid, Christodoulides said, "Israel, the prime minister himself, is in favor of our initiative."
"We are discussing the details... because the maritime area around Gaza does not allow for ships to approach," he said.
Last week, Cyprus Foreign Minister Constantinos Kombos visited Jordan and the Palestinian Authority in Ramallah in the occupied West Bank.
Christodoulides has also involved Egypt's President Abdel Fattah al-Sisi in the talks.
Cyprus already serves as a transit hub for foreign nationals evacuated from Israel because of the war.
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