Kabul was gridlocked as streets were sealed off around Rabbani's home, where ex-colleagues arrived to pay respects.
Rabbani, head of the council charged with talking to the Taliban, was killed by a bomb hidden in a turban.
President Hamid Karzai has cut short his visit to the UN in New York to return to Afghanistan.
Former warlords were among those paying respects, he says, arriving in cars with blackened windows.
There was heavy security in Kabul's diplomatic zone, where Rabbani's house is located, with police searching all those arriving.
Several hundred people, many wearing black headbands, carried pictures of Rabbani and chanted Koran verses.
Muslim tradition requires an immediate burial. There will be a special ceremony in the presidential palace before Rabbani's body is taken to his home province of Badakhshan in the north-east.
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