Across the valley you can see the airport, held by the UN, and the main barracks next to it, the last stronghold of government forces. This city is ringed with hills and the RPF controls them. The rebel movement also controls all the roads out of the city except one.
Every minute you can hear the boom of heavy artillery and the occasional crackle of machine guns but the rebels are not yet mounting a frontal assault. Nearby is a 12-barrelled Katuyusha rocket launcher and other artillery is being brought up. The advance has been hampered by the heavy rain which falls daily, and each officer has his own batman carrying his golf umbrella - their conspicuousness does not seem to worry them.
The officers, tall, brown-
skinned, all of them Tutsi, are relaxed, pointing out landmarks with sticks. As usual they are taking their time. They know that last road out of Kigali, the road south to Butare, is being cut by an advance some 50 miles south. It is only a matter of time before its stranglehold is complete and the city falls.
The RPF is going for broke. It is refusing to negotiate with the government and opposing the deployment of a UN force to stop the fighting. 'It is possible to discuss with the armed forces how to stop the killing of civilians, but we should not negotiate with a government which is destroying its own people,' said Patrick Mazimhaka, the first vice-president of the RPF. 'There is no one who we trust in the government . . . we had a peace agreement which we believed they accepted. A ceasefire now would simply stop us dealing with the government killing machine.'
It is difficult to find words for the enormity of this killing. The actual fighting has been drowned out by the massacres. It is like a football match in which the spectators have been slaughtered, making the game a sideline. But only the end of the game will end the killings and the RPF knows unless it takes over the country quickly the killings will continue.
There is a saying in Rwanda: 'When you kill the rats you do not leave the pregnant one alive.' The killers have obeyed this advice. In the piles of bodies - in churches and scattered around villages and along the road south - there are babies and children and women and men and the old. Approach any settlement in this country now and you smell it - the sweet and rotten smell of corpses.
Whole families have been wiped out by the gangs of killers armed with grenades, rifles, spears and machetes. In the church near Gahini, a small mission station and hospital, the bodies lie three or four deep. The people had taken refuge, but grenades were thrown in and the survivors finished off with machetes. Many of the corpses have the backs of the heads hacked off, others have had their feet chopped off and been left to die slowly.
This was not a spontaneous outburst of ethnic violence: Hutu against Tutsi. It was planned a long time ago. After the signing of the Arusha Peace Agreement in August 1993, President Juvenal Habyarimana was supposed to form a coalition government with the RPF. But he dodged and delayed, meanwhile setting up local militias through the youth wing of the Coalition pour la Defense de la Republique (CDR), a party which believes in Hutu exclusivity. 'We told the UN about these militias at the end of 1992,' said Mr Mazimhaka. 'We asked what are they for? The UN did nothing.'
Since then the Hutu extremists have tried twice to spark the militias into action. Last year they tried, and again in February after the killing of the Prime Minister. A few killings took place but it did not spread. Then after Habyarimana was killed when his plane was shot down on 6 April the country ignited. The 'Interahamwe' - 'those that attack together' - went into action throughout Rwanda targeting anyone known to be sympathetic to any other political party and all Tutsis.
It is not difficult to know who is who. Everyone in Rwanda has to carry an identity card which names his ethnic group, Hutu or Tutsi. The Interahamwe were coordinated by local commune heads and those who refused to carry out the killings were replaced. According to refugees from Murambi commune the mayor, known as Gatete, was replaced after the Arusha Agreement because he had organised killings of Tutsis in the past. Last month he was brought back and led the killings.
A blank-eyed 12-year-old boy, Karangwa, who had crept back into Rwanda alone from Tanzania, told me how a gang had come to his home armed with machetes, clubs and spears. They killed his parents and all his brothers and sisters. He had escaped with an uncle whose family was also wiped out. He thought they were the only survivors from five Tutsi families in the commune.
In areas near rivers people were simply tied up and thrown in. Their bodies have been swept eastwards, and at Rusumo Falls on Friday they were still coming at the rate of about one a minute. 'It has died down,' said one RPF guard there. 'Earlier in the week it was about 20 a minute.'
The figure of 250,000 is not hard to extrapolate from the known evidence but the sheer physical effort of killing so many people is hard to imagine. What will the RPF take over when it wins the war? Its politics are non-sectarian, though all its officers and most of its fighters are Tutsi. The Hutus who have fled before the RPF advance believe that it will kill them and drive them out. However disciplined and decent the RPF is, it not seen as a liberating force by the Hutus.
At one time the Tutsis were thought to make up between 10 and 15 per cent of the total population of 6 million: who knows how many are now left? As they advance westwards, the Tutsi officers of the RPF may find that the Hutus continue to flee before them, and that all their fellow Tutsis are dead.