Doctors in Atlanta have told the 91-year-old the tumours in his brain are being treated successfully and there are no signs of further cancer growth.
However, the spokeswoman said that doctors will continue tests.
Mr Carter, who served as president of the US from 1977 to 1981 and won a Nobel Peace Prize in 2002, announced his illness in August.
He said then he would receive radiation and chemotherapy for four tumours that had formed in his brain.
Media reports have suggested that Mr Carter was not experiencing any pain or discomfort during the treatments, and that his work with The Carter Center had not been scaled back.
The former president had been planning to travel to Nepal this month for volunteer work, but the trip was cancelled due to "civil unrest" in the country.

Unite said workers at the Atomic Weapons Establishment's (AWE) two Berkshire sites would strike for 12 days over a pensions dispute.
AWE, which builds the UK's Trident submarine warheads, said it had put "resilient measures in place".
It added that its pension scheme was "very competitive".
The walk-out of around 700 workers at Aldermaston and Burghfield in June, July, August and September will bring the number of strike days since November to 30.
Unite regional officer Bob Middleton said: "We know that our members' action has caused serious disruption to the production of the Trident warheads.
"We also know that convoys to Scotland carrying the missiles have been limited."
The dispute centres on Unite's claim that promises about pensions were broken after the scheme was moved to the private sector in the 1990s.
An AWE spokesperson said: "We are actively seeking to re-engage with Unite to find a positive resolution to this dispute."
The union Prospect agreed a pension settlement for its AWE members in February.

The clever machine dishes up six delicious flavours of ice cream with a variety of toppings.
One day robots may become sentient and take over the world. Until then, we're free to boss them about, so we want to know: What job would you give a robot?
Perhaps you'd make robots clean your room, or prepare delicious snacks?
I would make a robot clean the dishes and make beds!
Gabrielle, Birmingham, England
I would make my robot cook for me and do my homework for me.
Jessica, London, England
I would like a robot to work in mines so people don't have to go underground. I would also like a robot that sorts out my Lego bricks.
Jack, Swindon, Wiltshire
My robot would help me with my home work.
Aidan, Beckenham, England

Bangor Crematorium's chapel will be shut from 5-24 September.
Funerals will not be held but cremations can still be carried out while improvements are made to keep the facility up to standard.
Crematoriums in Colwyn Bay and Aberystwyth have been told about the closure and to expect more funerals at those facilities.
Gwynedd council's cabinet member for the environment, John Wynn Jones, said: "Every effort is made to minimise such work on the efficient running of the facility, however on this occasion the scale and location of the work combined with the need to remove asbestos materials means that we unfortunately have no option but to temporarily close the chapel facility."
Former US President Jimmy Carter is responding well to cancer treatment, according to his spokeswoman.
[NEXT_CONCEPT]
A union claims strikes have resulted in "serious disruption" to the UK's nuclear weapons programme as it announced further industrial action.
[NEXT_CONCEPT]
A robot that can serve ice cream has been revealed at a shopping centre in China.
[NEXT_CONCEPT]
A crematorium's chapel in Gwynedd will close for three weeks for asbestos removal and repair work.