Last night, they handed in a petition at Downing Street, asking Tony Blair to join the international call for President Clinton to release Peltier, by granting him "executive clemency". Peltier, who has exhausted all legal appeals, recently began his 24th year of imprisonment and will not be eligible for parole until 2008.
His health is failing - a long-standing jaw problem has now become so severe and painful that he cannot open his mouth enough to bite or chew his food - and his supporters fear he will die in his cell at the tough Leavenworth penitentiary in Kansas.
A Foreign Office spokesman said it had received representations from Peltier's supporters, passed on by Mr Blair, as well as several MPs, and would decide on its response after assessing the legal situation.
Peltier, 55, is serving two consecutive life sentences for the shootings at the Pine Ridge Indian Reservation in South Dakota. He has always denied the crime and those campaigning on his behalf consider him to be the victim of one of the greatest miscarriages of justice in US legal history.
His story was the inspiration for the film Thunderheart, which starred Val Kilmer as a young FBI agent who uncovers evidence of bureau misdeeds and learns the harsh reality of reservation life during a homicide investigation. Robert Redford has made a documentary about the case, and Peltier's plight has attracted support from Nelson Mandela, The Archbishop of Canterbury and Rev Jesse Jackson, as well as leading British and European politicians.
The shootings took place against a background of escalating tension between the militant American Indian Movement and the elected tribal government, which traditionalists on the reservation considered corrupt and a puppet of President Gerald Ford's administration.
The AIM emerged in the late 1960s to champion Indian rights, amid concern that the tribal government was failing to protect Indian lands - rich in natural reserves such as uranium - from developers. In 1973, traditionalists at Pine Ridge asked the AIM for protection when a paramilitary group, which supported the tribal government, allegedly began a campaign of terror.
Between 1973 and 1975 more than 60 Indians were killed and hundreds more assaulted and harassed, allegedly by the paramilitaries, whom the traditionalists claimed were backed by the FBI. On the day of the shootings the FBI agents had entered the reservation to find four people wanted on charges of assault and theft. Peltier admits firing a gun but denies killing the wounded agents at close range. Two other AIM leaders were acquitted of the killings, on the grounds of self-defence, after successfully arguing that the atmosphere of terror on the reservation explained their opening fire.
Following Peltier's conviction, it was revealed that the FBI had fabricated evidence from an alleged eyewitness, Myrtle Poor Bear, to secure his extradition from Canada, where he had fled after the gun battle. Her testimony was not used at the trial. In addition, ballistics and other evidence which may have been favourable to his case were also withheld.
An independent barrister consulted by Amnesty International found Peltier's conviction to be "unsafe and unsatisfactory" because the judge had refused to allow the introduction of evidence of serious FBI misconduct relating to the intimidation of witnesses, including Myrtle Poor Bear. This, it is claimed, would have cast serious doubt on the reliability of the main prosecution witnesses at the trial.
In 1986, the United States Court of Appeal ruled that the prosecution had omitted evidence but concluded this would not have affected the outcome of the trial. But one of the appeal judges, Gerald Heaney, later said the fact that the FBI had used improper tactics in its investigation should be considered in any petition for leniency.
He criticised the government for its earlier military response to "the legitimate grievances of the Native Americans", adding: "While the government's role in escalating the conflict into a firefight cannot serve as a legal justification for the killing of the FBI agents at short range, it can properly be considered as a mitigating circumstance."
Amnesty International recently accepted that a retrial was no longer feasible and is now asking for the President to intervene in the case.