Speaking to reporters aboard a military plane as he flew to the biennial NATO summit in Warsaw, which President Barack Obama will also attend,
Carter said alliance members have welcomed Obama's decision to keep 8,400 US troops in Afghanistan through the end of his term in office.
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Most US forces in Afghanistan are operating as part of NATO's Operation Resolute Support. In all, 39 NATO nations and partners contribute to the overall force of about 13,000.
Many NATO countries have "indicated the need to stick with the Resolute Support mission and to do more than they might have anticipated in past years," Carter said.
"A number of them have indicated they will be making those contributions, and I think the president will hear from other heads of state in NATO about what they are willing to do also in the future years. That's going to be an important outcome of the summit."
NATO Secretary-General Jens Stoltenberg on Wednesday said he supported Obama's announcement.
Most of the NATO troops in Afghanistan are working as advisors to local Afghan security forces.
Despite having about 320,000 troops and police officers, the Afghan forces have struggled to control the Taliban and have at times buckled under institutional failings such as deeply rooted corruption.
Carter said the extra US troops will allow Afghan forces to "reset" at the end of this summer's fighting season and get extra training over the winter.
The Afghan issue is one of three main crises confronting NATO at this year's summit.
Leaders must also grapple with the ongoing jihadist threat in Iraq and Syria and its concurrent refugee crisis, as well as aggressive posturing by Russia along the border with Eastern Europe.
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