Peskov reported that Putin and Trump spoke for an hour and a half.
He also confirmed that they had agreed to organize a personal meeting. Putin invited Trump to Moscow.
Putin also agreed with Trump that a long-term settlement in Ukraine can be achieved through negotiations, Peskov added.
The full text of the Kremlin press service's statement on Putin's conversation with Trump:
"The heads of state discussed issues related to the exchange of citizens of Russia and the United States. The President of the United States assured that the American side will fulfill all the agreements reached.
The topic of the settlement in Ukraine was also discussed. D. Trump spoke in favor of a quick cessation of hostilities and a peaceful resolution of the problem. V. Putin, for his part, mentioned the need to eliminate the root causes of the conflict and agreed with D. Trump that a long-term settlement can be achieved through peaceful negotiations.
The Russian President also supported one of the main theses of the American head of state, that it is time for our countries to work together.
During the conversation, the topics of the Middle East settlement, the Iranian nuclear program, as well as bilateral Russian-American relations in the economic sphere were raised.
The Russian President invited the US President to visit Moscow and expressed his readiness to receive American officials in Russia on areas of mutual interest, including the Ukrainian settlement.
"V. Putin and D. Trump agreed to continue personal contacts, including organizing personal meetings."