Demoralised government troops fell back in parts of the city ahead of a steady rebel advance, and United Nations officials said it appeared to be only a matter of days before the RPF took Kigali.
Rebel infantrymen, following behind intense barrages of artillery and mortar fire, inched forward in fierce combat that appeared to be street-to-street in parts of the city centre.
Both sides suffered heavy casualties during two days of fighting near the airport, said UN spokesman Abdul Kabia.
Fighting halted or delayed deliveries of food and water for a second day to thousands of displaced people living under UN protection because of the bloodbath mainly between majority Hutus and minority Tutsis.
The United States, in its first military involvement in Africa since pulling out of the 15-month operation in Somalia, announced yesterday it had started flying relief supplies to Rwandan refugees in Tanzania.
The US embassy in Nairobi said 15 Starlifter C-141 military planes were flying supplies to nearly 250,000 Rwandan refugees in Tanzania and Burundi. It said further flights were possible.
An afternoon lull allowed delivery of some relief supplies to 3,000 people sheltered at the stadium in Kigali and permitted one UN aid flight to land at the airport.
Despite resistance by the Hutu-led army, the mainly Tutsi rebels fought their way closer to Ruhengeri, 70km (43 miles) north- west of Kigali. Rebels also reportedly were meeting heavy resistance near Bugasera, 25km south- east of Kigali, where the offensive paused while the RPF manoeuvred to consolidate its gains.
The UN High Commissioner for Refugees issued an emergency appeal yesterday for donations of dollars 56.7m ( pounds 38m) to aid more than 800,000 refugees from Rwanda and Burundi. The main focus is the 250,000 Rwandans at the Benaco camp in Tanzania. Overnight this became the largest such camp in the world after refugees fled across the Rusumo bridge to escape the savagery in Rwanda.
In Geneva, a UNHCR spokesman said 400 to 1,500 refugees arrived at the camp each day.
The wounded heart, page 19