NAYPYITAW (Reuters) - U.S. Secretary of State Rex Tillerson called on Wednesday for a credible investigation into reports of human rights abuses against Rohingya Muslims committed by Myanmar s security forces after a meeting with its civilian and military leaders. More than 600,000 Rohingya Muslims have fled to Bangladesh since late August, driven out by a military counter-insurgency clearance operation in Buddhist-majority Myanmar s Rakhine State.  A top U.N. official has described the military s actions as a textbook case of  ethnic cleansing .  We re deeply concerned by credible reports of widespread atrocities committed by Myanmar s security forces and by vigilantes who were unrestrained by the security forces during the recent violence in Rakhine State,  Tillerson told a joint news conference with Aung San Suu Kyi, the head of a civilian administration that is less than two years old and shares power with the military. Tillerson had earlier held separate talks with Myanmar s military chief, Senior General Min Aung Hlaing, whose forces have been accused of atrocities. A senior U.N. official on Sunday leveled allegations of mass rape, killings and torture against the Myanmar military, known as the Tatmadaw, after a tour of refugee camps in the Cox s Bazar region of neighboring Bangladesh. Tillerson called for the Myanmar government to lead a credible and impartial investigation and said those who committed abuses should be held responsible.  The recent serious allegations of abuses in Rakhine state demand a credible and impartial investigation and those who commit human rights abuses or violations must be held accountable,  he said.  In all my meetings, I have called on the Myanmar civilian government to lead a full and effective independent investigation and for the military to facilitate full access and cooperation.  He also said it was the duty of the military to help the government to meet commitments to ensure the safety and security of all people in Rakhine state. A posting on Min Aung Hlaing s Facebook page said Myanmar s military supremo had explained to Tillerson the  true situation in Rakhine , the reasons why Muslims fled, how the military was working with the government to deliver aid and the progress made for a repatriation process to be agreed with Bangladesh. The military launched its clearance operation after an army base and 30 police posts were attacked on Aug. 25 by Rohingya militants, killing about a dozen members of the security forces. Tillerson condemned the militant attacks, but said any response by the security forces needed to avoid to the  maximum extent possible harming innocent civilians . An internal investigation by the military into the  allegations of atrocities that was released this week was branded a  whitewash  by human rights groups. Back in Washington, U.S. senators are pressing for economic sanctions and travel restrictions targeting the Myanmar military and its business interests. Tillerson said he would advise against any broad-based sanctions against Myanmar, as the United States wanted to see it succeed. But he said if there was credible and reliable information on abuses by individuals they could be targeted by sanctions. Tillerson said the United States would work with partners so that those responsible for any atrocities would face consequences,  using all available mechanisms, including those available under U.S. law . Myanmar is undergoing a transition to democracy after decades of rule by the military, but the generals retain extensive powers over security and a veto over reform of a constitution that has barred Suu Kyi from the presidency.  Myanmar s response to this crisis is critical to determining the success of its transition to a more democratic society,  Tillerson said.   It s a responsibility of the government and its security forces to protect and respect the human rights of all persons within its borders and to hold accountable those who fail to do so.  He said the United States would provide an additional $47 million in humanitarian assistance for refugees bringing the total to $87 million since the crisis erupted in August.  The humanitarian scale of this crisis is staggering,  Tillerson said. But he said he was encouraged by talks between Myanmar and Bangladesh to agree on a refugee repatriation process. During the news conference, Suu Kyi was asked to explain why she had not spoken out more strongly over the plight of the Rohingya, as the Nobel peace prize winner s perceived failure to speak up has damaged her international reputation as a stateswoman.  What I say is not supposed to be exciting,  Suu Kyi said, adding that she had aimed to keep the public informed without setting different ethnic, religious communities against each other.  It s important to bring peace and stability to this country and that can only be done on the basis of rule of law and everybody should understand that the role of theirs is to protect peace and stability, not to punish people.     