Speaking after the phone call with the Russian President, US President Donald Trump said: " should have said very strongly that President Putin will have to respond to the recent attack on airports."
Mr. Trump warned in a social media post that a more than hour-long phone call between the two Russian and US leaders would not "lead to immediate peace" between Russia and Ukraine.
The two leaders also discussed Iran, in which Mr. Trump said that Mr. Putin suggested that it could help negotiate nuclear with Iran.
Russian state news agency RIA Novosti said that Mr. Putin told Mr. Trump that Ukraine had sought to disrupt peace negotiations.
The two leaders also "exchanged views on the prospects for restoring cooperation between the two countries, which has great potential".
This is the first time President Putin and President Trump have held a phone call since Ukraine launched a surprise attack by drones on Russian air bases on June 1, targeting long-range bombers capable of carrying nuclear weapons.
The Kremlin later confirmed on June 4 that Trump had told Putin that the US was not given any advance warnings about the attack.