The devastation threatens numerous species
"A lot of it is illegal logging in areas of the tropics," Mr Bryant told BBC Radio 4's Today programme.
"[There are] good rules on the books by governments who are really making an effort, but they're just not implemented on the ground," he said.
Two-year survey
The WRI report is based on a two-year survey that covered North America, Russia, Indonesia, Central Africa, Chile and Venezuela.
It found that areas believed to have forest land intact were now riddled with roads, logging and mining activity.
"As we examined what we thought were still vast, untouched stretches of intact forests in the world, we came to the conclusion that they are fast becoming a myth," WRI president Jonathan Lash said.
"We've mapped about half the world's forests in detail and we're finding that the closer we look, the less intact old growth and primary forest we're finding," said Mr Bryant.
Russian loss
"[That is] considerably less in many places than we had estimated during our original mapping several years ago," he added.
"Russia is a great example. [It is] the biggest forest area in the world in a single country.
"We found only a quarter of forests today are intact in larger tracts of old growth and primary forest," he said.
Such forest trees are important in counteracting climate change, Mr Bryant said.
"They store vast amounts of carbon, which, if you clear them, burn them and degrade them, then go into the atmosphere and contribute to global warming," he said.
Industry role
Mr Bryant did, however, have some words of optimism about deforestation.
"It's being offset to some extent by regenerating forests in certain parts of the world.
He said companies were also playing a role.
"Industry is stepping to the fore and leading companies are realising that through market investment decisions, they can make a difference."