"It would be irresponsible of us, as well as morally very difficult, to turn your back on a community fighting ISIL," he said during a visit to the Indonesian capital Jakarta, using an alternative name for the Islamic State group.
Kerry said the situation amounted to a "crisis moment" and insisted that the move was not a shift in policy.
He said Washington understood the challenges Turkey faces with respect to the rebel Kurdistan Workers Party (PKK), outlawed by Ankara.
The weapons were dropped by air because Ankara has refused to deliver arms by land to the Syrian Kurdish fighters defending Kobane, because they have links to the PKK.
"But we have undertaken a coalition effort to degrade and destroy ISIL. And ISIL is presenting itself in major numbers in this place called Kobane," said Kerry.
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"It is a crisis moment, an emergency where we clearly do not want to see Kobane become a horrible example of the unwillingness of people to be able to help those who are fighting ISIL."
Kerry said the United States' hope was that "Kurds who have proven themselves to be very strong and valiant fighters will take this fight on".
The US-led coalition has carried out more than 135 air strikes against IS targets around Kobane but it was the first time that it had delivered arms to the town's defenders.
Three C-130 cargo aircraft Monday carried out what US Central Command called "multiple" successful drops of supplies, including small arms, provided by Kurdish authorities in Iraq.
IS militants launched their offensive on Kurdish fighters around Kobane on September 15, but the Kurds have kept up a dogged resistance on the streets of the town, of which they currently control around half.
In a shift of policy, Ankara announced on Monday that it was helping Iraqi Kurdish fighters -- who are not linked to the PKK -- to reinforce the town against the jihadist offensive now nearly five weeks old.