MEXICO CITY, Aug 2 (Reuters) - Mexican police have arrested two lumberjacks accused of murdering an anti-logging activist, authorities said on Thursday, following criticism from environmental group Greenpeace of official foot-dragging.

A spokesman at the state attorney general's office said police arrested the two men, who are brothers, on Wednesday. Authorities are searching for two other men in connection with the May 15 killing.

Prosecutors called the detention proof the government is tackling illegal logging.

This "reiterates our commitment ... to fully combat impunity and delinquency in all its forms," the state attorney general's office said in a statement.

Illegal logging destroys some 64,000 acres (26,000 hectares) of Mexican forest each year, the government says, putting Mexico near the top of a U.N. list of countries losing primary forest fastest. Environmental activists say the figure is far higher.

Greenpeace, which has campaigned for the arrest of the loggers since the killing, welcomed the news but urged the government to capture the other suspects and end illegal logging in Mexico.

Aldo Zamora was gathering information for Greenpeace when four men identified by witnesses and police as brothers in a logging gang ambushed his car on a forest road in the State of Mexico and sprayed him with bullets.

The activists criticized the police for moving too slowly and allowing the suspects to go into hiding.

Earlier this year, President Felipe Calderon pledged "zero tolerance" against illegal loggers but environmentalists say the gangs enjoy ever greater protection.

Tree cutting is a lucrative source of cash for many impoverished indigenous communities in rural Mexico.

Greenpeace says nearly half the timber cut in Mexico is illegal, often harvested by gangs that terrorize villages into selling trees.

"While the members of these gangs are free, including Aldo's murderers, there will be no justice for the Zamora family or for the forests," the group announced.

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