* More than 340 villagers evacuated -police
* Police and military say tough measures could be taken
* Separatist group says two members injured in gunfighting
* Blames Freeport mine for deaths, environmental damage (Adds comment from separatist group)
By Fergus Jensen and Sam Wanda
JAKARTA/TIMIKA, Indonesia, Nov 17 (Reuters) - Indonesia on Friday began evacuating villages that authorities said had been occupied by armed separatists after a string of shootings near a huge copper mine operated by Freeport McMoRan Inc.
Two police have been killed and at least 12 people wounded by gunfire in the area, in the eastern province of Papua, since mid-August. Police have blamed an "armed criminal group" while military authorities say the gunmen were linked to separatist rebels.
According to police reports the group occupied Banti and Kimbely, two villages near the mining town of Tembagapura, and had prevented an estimated 1,300 residents from leaving, leading to food shortages.
The separatist West Papua National Liberation Army (TPN-OPM) has claimed responsibility for the shootings but denied its soldiers were in the villages or taking hostages.
It blames Freeport's presence for environmental destruction and the loss of Papuan lives in the area around Grasberg, the world's second largest copper mine by volume.
Police and military leaders said they had urged the gunmen to surrender, warning that tough measures could otherwise follow.
Residents were being evacuated to a sports hall in Tembagapura, according to a source at Freeport. Police said more than 340 were evacuated and the area had been secured.
"We hope they can return safely to their respective villages," Papua Police chief Boy Rafli Amar said in a video of the evacuation distributed by police.
"During the rescue mission, there was an exchange of fire from morning to midday," police spokesman Ahmad Mustofa Kamal told Reuters.
Reuters was unable to confirm reports on social media of civilian casualties.
TPN-OPM Commander Hendrik Wanmang told Reuters the group's aim was to "destroy Freeport".
"If the Indonesian police and military want to be in the villages of Banti or Kimbely that doesn't matter," he said. "This is a war to defend a nation and separate ourselves from the Unitary State of the Republic of Indonesia.
Two TPN soldiers were injured in gunfire on Friday, he said.
According to the group, which is linked to the Free Papua Movement, Freeport's presence had led to the "intimidation, rape and extermination of thousands of Papuan people", as well as destruction of the natural environment and wildlife.
A spokesman for Freeport Indonesia declined to comment.
The company says on its website it is committed to ensuring its activities are "in line with the U.N. Universal Declaration of Human Rights, the laws and regulations of Indonesia, and the cultures of communities native to operating areas of our company".
It also ensures that "environmental considerations are an integral part of all planning, engineering and operations".
According to several residents interviewed by Reuters, military and police officers were preventing them from getting food from Tembagapura, where aid was delivered on Saturday.
"The atmosphere has really heated up," one resident said, referring to the shootings and concerns over food and safety.
The Grasberg mine has been dogged by security concerns for decades, as pro-independence rebels have waged a low-level conflict in Papua. Between 2009 and 2015, shootings in the mine project area killed 20 people.
Reporting by Sam Wanda in TIMIKA and Fergus Jensen in JAKARTA; Editing by Nick Macfie and John Stonestreet