Abdullah said Musa Aman, the chief minister in Malaysia's Sabah state, will not "easily give licences so that he can protect the rainforest."
"If anyone requests for forest concession for timber logging, I will say no, and I know Musa will say no," Abdullah was quoted by the official Bernama news agency as saying.
He said government has taken steps to promote sustainable forest management, with timber companies required to pass stringent certification procedures.
About 60 percent of Malaysia's total land area, or about 19.52 million hectares, will remain as forested sections, Abdullah said.
"We must defend this because we get a lot of benefits from the tropical forests, like medicines and so forth," he added.
The World Wildlife Fund (WWF) on Thursday said that about 40 percent of the forest cover in Sabah, in the Malaysian part of Borneo island, has been lost to logging, palm oil plantation and human settlement.
It said human encroachment on forests was also threatening wildlife, including the pygmy elephants unique to Borneo, whose numbers are falling.
Meanwhile, indigenous communities are also furious over major infrastructure projects that force them out of ancestral lands into forced relocation.