"We can propose again that the European Union, European countries, monitor this passage in a very strict manner," Kouchner told reporters after meeting his British counterpart William Hague.
"We can very well monitor the cargoes of ships going to Gaza. We can do it, we’d like to do it, we’d be very happy about doing it," he said, adding that the situation in Gaza was "untenable".
France and Britain offered to send warships to monitor and prevent arms smuggling to Gaza following Israel’s 22-day offensive in the Palestinian Hamas-ruled territory that ended in January last year.
European Union monitors helped oversee the Rafah land crossing point into Gaza until 2007, when the operation was suspended for security reasons. Although the mission is currently inactive, its mandate was extended for another year by EU leaders last month.
Hague, who was beginning a tour of European capitals which will take him to Rome, Berlin and Warsaw, said he had held extensive discussions with partners about how to ensure that "aid and normal economic flows are possible into Gaza without, of course, an even greater flow of weapons."
"I think the EU can help in that as it has in the past," he said.
Both ministers also called on Israel to accept an international inquiry into last week’s interception of the flotilla trying to bring supplies to Gaza.
"We think it is very important that there is a prompt and impartial and credible and transparent investigation into the events of last Monday with the Gaza flotilla," Hague said, referring to the deaths of the pro-Palestinian activists on board the Mavi Marmara, boarded by Israeli commandos.
"And we believe there should be an international presence at minimum in that inquiry or investigation and that is what I said to the Israeli government again today."
'International inquiry in Israel’s interest'
Earlier on Sunday, Israel’s ambassador to the United States said his government did not want an international inquiry to investigate the raid but was discussing options with Washington.
Kouchner said a broad, international inquiry was in Israel’s own best interest.
"It’s up to them to respond but I think that quite a precise proposal has already been made by the Americans, the French and the United Nations," he said.
Prime Minister Benjamin Netanyahu spoke with world leaders on Sunday evening in a bid to ease the pressure on Israel, including US Vice President Joe Biden, French President Nicolas Sarkozy and Quartet envoy to the Middle East Tony Blair.
Sarkozy asked Netanyahu to "accept the UN Security Council's demand and agree to a reliable and impartial committee of inquiry in regards to Israel's operation against the 'freedom sail.'" He also called on Israel and the Palestinians to resume peace negotiations "based on a solution of two states living side by side in peace and security."
Netanyahu, who also spoke with the Canadian and Georgian prime ministers, and earlier with the Bulgarian and Greek prime ministers, stressed that "Israel acted on this matter just like any country attacked with thousands of missiles and rockets would have acted and maintains its right to self defense."
Roni Sofer contributed to this report