Mr Obama had expressed his gratitude to Mr Key for chairing the meeting.
Mr Key and Mr Obama were elected to power within weeks of each other in 2008.
Asked what their relationship was like, Mr Key said:"it's really warm. We know each other pretty well. We've been to lots of things together over the course of the last five years.
He seems very relaxed and comfortable. It's not stuffy. It's conversational and casual. "
Trade negotiators are due to meet in Singapore in the next week to start a more I tense negotiating programme to meet the deadline.
Mr Key chaired a meeting of 12 TPP countries at Apec in Bali in Mr Obama's place.
It reaffirmed the goal to have the free trade and investment treaty finished by the end of the year.
The US Federal Budget crisis meant Mr Obama had to cancel his trip.
The White House has issued a statement about Mr Obama's phone call, in which he thanked Mr Key for chairing the talks.
The statement said the President called Mr Key "to thank him for successfully chairing the meeting ... and to discuss the productive outcomes".
"The two leaders welcomed the agreement among leaders that the 12 member nations will work toward the ambitious goal of concluding negotiations this year, and they committed to intensifying efforts to reach that goal."
The statement said "this comprehensive and high standard agreement is a model for future trade agreements and a promising pathway to our APEC goal of building a Free Trade Area of the Asia Pacific".
The 12 countries are New Zealand, United States, Australia, Mexico, Canada, Peru, Chile, Malaysia, Brunei, Singapore, Vietnam, and Japan.