This is at least five million years earlier than fossil evidence has so far been able to show, according to a team of scientists from the United States, Australia and Tanzania.
"These discoveries suggest that the members of the major primate groups that today include apes and Old World monkeys were sharing the planet millions of years earlier than previously documented," said study co-author Nancy Stevens of Ohio University.
Old World monkeys (cercopithecoids) like baboons and macaques are found in Africa and Asia today, and are a distinct group from American or New World monkeys like marmosets and spider monkeys.
Scientists analysing modern primate DNA had already predicted that apes and monkeys must have split from a common primate ancestor about 25 to 30 million years ago, but the evidence has been lacking -- the oldest fossils found to date were some 20 million years old.
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The new skull fragments, dug up in the Rukwa Rift Basin of Tanzania in 2011 and 2012, belonged to a previously unknown monkey named Nsungwepithecus gunnelli, and an ape dubbed Rukwapithecus fleaglei.
The team scanned the specimens and created 3-D reconstructions that they compared to other fossils.
Stevens said Rukwapithecus would have been an ape weighing about 12 kilogrammes.
"Because of its more fragmentary nature, it is more difficult to assess the body mass of Nsungwepithecus, but it would likely have been a bit smaller," she told AFP.
Both date from the Oligocene period, which lasted from 34 to 23 million years ago.