More than 2,100 people have died since the magnitude 6.8 earthquake hit Morocco on Friday.
When asked why Morocco had not made an official request to Paris for urgent assistance, Catherine Colonna told BFM television on Monday, “We are ready to help Morocco. It’s a sovereign Moroccan decision, and it’s up to them to decide.”
She described the situation so far as a “misplaced controversy”.
On Monday, Colonna announced that Paris has made 5 million euros ($5.4m) available for non-governmental organisations operating in Morocco.
But Rabat has been selective with the aid it receives and has so far accepted help from Spain, the United Kingdom, Qatar and the United Arab Emirates only.
On Friday night, a magnitude 6.8 earthquake hit Morocco.
There were at least four French citizens among the thousands of victims.
According to the US Geological Survey, no earthquakes have been stronger than a magnitude of 6.0 within 310 miles (500km) of the epicentre of Friday’s quake in at least a century.
The shock cracked and levelled parts of the walls surrounding Marrakesh’s old city, a UNESCO World Heritage Site built in the 12th century.
Al Jazeera’s Jonah Hull, reporting from Marrakesh, said the deaths and injuries were rising the fastest in remote, mountainous areas.
“Bodies lie in the open air covered by blankets. In some cases, mass graves are being dug as funerals are held, and of course, vital supplies are running out,” he said.
On Sunday, the head of a French rescue charity said Moroccan authorities prevented its teams trying to provide emergency aid from entering the country.
Arnaud Fraisse, head of the Secouristes Sans Frontieres (Rescuers Without Borders) organisation, told France Inter broadcaster that aid workers had hoped to get on a flight to Morocco on Sunday.
“Unfortunately, we still don’t have the go-ahead from the Moroccan government,” he said.
French officials have tried to play down any rift between the two countries, which is centred on the issue of Western Sahara, which Morocco wants France to recognise as Moroccan.
Relations have also been tested amid French President Emmanuel Macron’s efforts to forge closer ties with Algeria.
At the time of the disaster, Morocco’s King Mohammed VI was reportedly in France.
Interior Minister Gerald Darmanin told France 2 TV earlier on Monday that Morocco, a “brotherly” nation, could cope alone with the rescue efforts.
More than 51,000 French citizens live in Morocco, according to the Ministry for Europe and Foreign Affairs figures.
The Observatory for Immigration and Demographics, France has a Moroccan diaspora of about 1.5 million people, including 670 dual nationals.