Story highlights Those who work for 'undesirable' NGOs could face six years in prison

U.S. State Department says it is "deeply disturbed" by new law

Law says any organization posing threat to country's security can be designated undesirable

(CNN) Non-governmental organizations working in Russia awoke Sunday to a new reality -- that they operate now under a law that allows the government to prosecute them on the grounds they are 'undesirable.'

And those who work for such organizations could be sentenced to as much as six years in prison.

The new measure, signed into law Saturday by President Vladimir Putin, has provoked an international outcry.

The U.S. State Department said it was "deeply troubled." Amnesty International said the law threatened "fundamental freedoms." Human Rights Watch called it a "piece of repressive legislation."

'Threat to the constitutional order'

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