Obama said the deal includes "substantial limitations which will prevent Iran from building a nuclear weapon."
Even so, Zarif said Sunday's deal with world powers contained a "clear reference that (uranium) enrichment will continue."
"The burden is on Iran to prove to the world that its nuclear program will be exclusively for peaceful purposes," Obama said in his address.
The deal includes an agreement that Iran will halt some progress on its nuclear program, including a plutonium reactor at the Arak facility. The deal also reportedly calls on Iran to neutralize its 20 percent enriched uranium stockpiles.
Iran will suspend its enrichment of all uranium above 5 percent.
Iran has further committed to halt its expansion of the nation's uranium enrichment program, halt the installation of additional centrifuges and ban the use of advanced centrifuges.
In addition, Tehran has agreed to intrusive inspections under the terms of the deal.
"We will gain daily access to key facilities," Secretary of State John Kerry said at a news conference on the deal in Geneva.
In the interim, Obama promised that the U.S. "will refrain from imposing new sanctions and allow the Iranian government a portion of the revenue" it was previously denied.
Still, he said, "If Iran does not fully meet its commitments in six months, we will turn off the relief and crank up the pressure."
Zarif indicated in comments early Sunday that in the final step of negotiations, set to take place in six months, negotiators will achieve a comprehensive deal on Iran's enrichment program when all sanctions are lifted.
The U.S. maintained the controversial sanctions had always been a measure aimed at bringing about the kind of agreement reached in Geneva.
"Make no mistake, and I ask you, don't interpret that the sanctions were an end unto themselves. The goal of the sanction was always to have a negotiation," Kerry said.
Obama said that if Iran breaks its promise, it will face more of a backlash from the U.S.
"Because of its record violating obligations, Iran must accept strict limitations on its nuclear program," Obama said.
Top European Union diplomat Catherine Ashton told Reuters the deal would create the time and space for a more comprehensive deal on Iran’s nuclear program.
Obama and Kerry sought to reassure international allies, including Israel, that commitments to their safety would remain unchanged by the deal.
Still, Israel's Prime Minister Benjamin Netanyahu called the agreement "a bad deal."
"No deal is better than a bad deal," Kerry said, expressing confidence in the agreement.
Kerry and his counterparts from Russia, Britain, France, China and Germany joined the Geneva talks after Zarif and Ashton reported progress on uranium enrichment and other issues on Friday.
The diplomats had aimed to hammer out an agreement to freeze Iran's nuclear program for six months, while offering the Iranians limited relief from crippling economic sanctions. If the interim deal holds, the parties will negotiate final-stage agreements to ensure Iran does not build nuclear weapons.
Al Jazeera and wire services