MOSCOW/WASHINGTON (Reuters) - Russian President Vladimir Putin and U.S. President Barack Obama discussed the Syrian war in a phone call on Wednesday and the Kremlin said both leaders confirmed they were ready to increase coordination of military action in Syria.

U.S. President Barack Obama and Russian President Vladimir Putin meet at the United Nations General Assembly in New York September 28, 2015. REUTERS/Kevin Lamarque

The White House said Obama stressed the need for Russia to press the Damascus government to halt attacks on civilians and for progress to be made on a political transition to end the war in Syria.

Relations between Russia and the United States have been strained by disagreements over the conflict in Syria, where Moscow and Washington are backing opposing sides in the civil war.

The Kremlin said in a statement that Putin had used the call to urge Obama to aid the separation of the “moderate” opposition in Syria from the Nusra Front and other “extremist” groups.

In its statement on the call, the White House said the two leaders confirmed their commitment to defeat Islamic State and Nusra Front.

The Kremlin statement said the phone call took place on the initiative of Russia and that both sides also stressed the importance of United Nations-brokered peace talks restarting.

“President Obama also stressed the necessity for progress on a genuine political transition to end the conflict in Syria, as well as sustained humanitarian access,” the White House statement said.

The two leaders also discussed the conflicts in Ukraine and Nagorno-Karabakh, according to the two statements.

Obama urged Putin “to take steps to end the significant uptick in fighting in eastern Ukraine” and stressed the need for full implementation of the Minsk agreements, the White House said.

Putin reiterated the Minsk peace agreements on Ukraine must be fulfilled by Kiev and said Russia wanted a peace process over Nagorno-Karabakh to progress, according to the Russian statement.

Obama said he was ready to intensify efforts together with Russia and France to achieve a comprehensive settlement of the Nagorno-Karabakh conflict between Azerbaijan and Armenian-backed separatists, the White House statement said.