But the senior army officers are expected to come under further pressure when Manila, following weeks of criticism and on Alston's recommendation, finally publishes the report of a government-created inquiry into the unsolved killing of hundreds of left-wing activists.
In a pre-emptive move ahead of the report's publication, the military released a copy of a letter Esperon wrote to Melo, rebutting his findings and calling his conclusions "strained, unfair and a blank accusation".
The government and the military have repeatedly blamed the armed communist group, the New People's Army (NPA), for the murders, saying the organisation is purging its ranks as it did to chilling effect in the late 1980s.
While Esperon has said the military will cooperate with any investigation into the murders, in his letter to Melo he said a formal internal probe would, "inevitably amount to a witch-hunt or fishing expedition".
He said: "The armed forces cannot and should not undertake any such activity."
Gloria Arroyo, the Philippines' president, has called for the creation of special courts to deal with the political killings and asked the armed forces to update its rules on command responsibility.
Esperon insisted on Thursday that the command procedure was sound.
The government has traditionally shied away from harsh punishment of the military, a powerful political force in the Philippines, where it has helped to oust two leaders and propel Arroyo to power in 2001.
Teodoro Casino, a legislator and member of the Bayan Muna group, whose members have been among those killed, said Esperon's letter was "a pathetic attempt at a whitewash".
Local rights group Karapatan has said more than 800 people, most of them left-wing activists, have been murdered or reported missing since 2001.
|"The only way to discourage executions is by punishing the perpetrators and showing that the state does not sanction murder"|
Editorial, The Philippine Star
Many of those killed are members of organisations the government views as fronts for the NPA, which has been waging a decades-long insurgency that has killed more than 40,000 people.
Arroyo declared an "all-out war" on the NPA last year and left-wing activists say the shootings of their colleagues, frequently carried out in daylight by masked men on motorbikes, is part of the government's counter-insurgency campaign.
Alston said there did not appear to be state sanction for the killings and Esperon has said troops do not use extra-judicial executions to deal with the "communist threat".
But the UN investigator's strong indictment of the military has provoked calls for the government to finally step in and stop the shootings.
An editorial in The Philippine Star said: "The only way to discourage executions is by punishing the perpetrators and showing that the state does not sanction murder."