Fighting appeared to have diminished after a fierce attack late yesterday by IS fighters, including suicide bombers, witnesses and monitors said.
IS forces in the east of the town were exchanging fire with Kurdish militia in the west and there were reports of an explosion, probably a car bomb, the Syrian Observatory for Human Rights monitoring group said.
Kobane has become a crucial symbolic battleground in the war against IS, which is fighting to extend areas under its control in Iraq and Syria where it has declared an Islamic "caliphate".
Iraqi Kurdish officials have said they will provide the training, although any forces sent will be Syrian Kurds.
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A local Kurdish official, Idris Nassen, told AFP Kobane was relatively calm today, adding that no reinforcements had yet arrived and they did not have "any idea" when they would.
Turkish Foreign Minister Mevlut Cavusoglu confirmed that Kurdish fighters had yet to cross from Turkey to Kobane, telling NTV television "the issue is still being discussed".
Three C-130 cargo aircraft carried out what the US military called "multiple" successful drops of supplies early yesterday, including arms provided by Kurdish authorities in Iraq.
A US-led coalition has carried out more than 140 air strikes against IS targets around Kobane, but it was the first time it had delivered arms to the town's defenders.
US Central Command said one of the 27 bundles had gone astray but that American warplanes bombed it to prevent it being snatched by IS.
Despite the Kobane operation, US commanders said the top priority remains Iraq, where IS swept through much of the Sunni Arab heartland north and west of Baghdad in June, with both government and Kurdish forces under pressure.