This climate change banner was first seen on a photo released by Greenpeace on 8 December.
However, in order to lay the banner down, the activists are alleged to have entered a "strictly prohibited" area and caused damage.
The Times reported that the Peruvian government is now seeking to stop the activists leaving the country and asking prosecutors to file charges of "attacking archaeological monuments", which would carry a six-year prison sentence.
Speaking to various news agencies, deputy culture minister Luis Jaime Castillo said:
It's a true slap in the face at everything Peruvians consider sacred. They are absolutely fragile. They are black rocks on a white background. You walk there and the footprint is going to last hundreds or thousands of years. ...
This has been done without any respect for our laws. It was done in the middle of the night. They went ahead and stepped on our hummingbird, and looking at the pictures we can see there's very severe damage. Nobody can go on these lines without permission – not even the president of Peru.
The BBC reported that Greenpeace has apologised.
In a statement, Greenpeace told the broadcaster:
Without reservation Greenpeace apologises to the people of Peru for the offence caused. ... We are deeply sorry for this.
We fully understand that this looks bad. Rather than relay an urgent message of hope and possibility to the leaders gathering at the Lima UN climate talks, we came across as careless and crass.
We have now met with the Peruvian culture ministry responsible for the site to offer an apology. We welcome any independent review of the consequences of our activity. We will co-operate fully with any investigation.