His family said the lack of communication since that date was “out of character”.
Relatives of the backpacker, from Bronygarth near Oswestry, are planning to travel to the country after a search of the area failed to leave any indication of his whereabouts.
Greaves had flown to Peru to meet friends in Pisac, near Cusco, on February 20 and had emailed his family twice saying he was enjoying his trip, reports BBC News.
On April 7 he told his friends of his plans to go on a mountain expedition in Kinsa Cocha by himself and expected to return by April 10.
"He’s done a number of outdoor trips before," his sister Ellen Greaves said.
"We understand he went with provisions - with a tent and food."
"We’ve contacted the Foreign Office here. Interpol now know all the details. And out there his friends have contacted the local police, local bus stations, local taxis," she added.
The family described Greaves as self-reliant and practical, and added it was "out of character [for him] to be out of touch for so long.”