FRANKFURT (Reuters) - Hospitals in the German state of Baden-Wuerttemberg have offered to treat some critically ill coronavirus patients from the neighboring Alsace region in France, which is struggling to cope with a rising number of cases.

Four teaching hospitals and an army hospital in the south-western German state will take in 10 French patients requiring ventilation, and the state is checking with other hospitals for more spare beds in intensive care units, Baden-Wuerttemberg's science and research ministry said in a statement on Saturday.

Doctors in the eastern French cities of Mulhouse and Colmar have warned that the healthcare system is at breaking point.

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The crisis in the east of the country led the French army to transfer six patients in critical condition due to coronavirus to a military facility on Wednesday.[L8N2BB3XX]

"We are sending a sign of solidarity to our French neighbors," state science minister Theresia Bauer said in the statement.

The ministry added, however, that there were limits to the state's hospital capacity and that help would be for as long as intensive-care beds were not needed by patients in closer vicinity.

It said that critically ill coronavirus patients needed ventilation for an average of three to seven days.

The French government on Tuesday put its 67 million people under lockdown, in an unprecedented act during peacetime, after an almost 20% rise in deaths and reported cases in just 24 hours, with eastern France the worst-hit region.