Putin has previously voiced "deep concern" over US President Donald Trump's decision and Russian officials have said they would work with European partners to preserve the agreement.
"The importance of preserving the deal from a point of view of international and regional stability was highlighted," the Kremlin said in a statement following a call between Putin and Merkel.
The two leaders also discussed the situation in Syria as well as Merkel's planned working visit to Russia next week, Moscow said.
Merkel has previously said Germany and its European partners would "do everything" to ensure Iran remains in the landmark 2015 nuclear deal.
The Russian president also spoke with his Turkish counterpart Erdogan, with the pair saying Trump was "wrong" to pull out of the accord, according to a Turkish presidential source late Thursday.
Ankara has been working closely with Moscow and Tehran over the past year on the Syrian peace process despite Turkey and Russia being on opposing sides of the conflict and having a sometimes troubled relationship with Iran.
Iran's Foreign Minister Mohammad Javad Zarif will visit Russia in the coming days as part of a diplomatic tour taking in Brussels and Beijing, his spokesman said Friday.
Trump this week defied the wishes of world powers when he announced that Washington would withdraw from the historic nuclear accord and impose new sanctions on Tehran.
After long negotiations, Iran had agreed in July 2015 to freeze its nuclear programme in return for the lifting of punishing international sanctions.
The deal had been negotiated between Iran and the five permanent members of the UN Security Council -- Britain, China, France, Russia and the United States -- plus Germany.
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