But Putin appeared not to be swayed by the French president's appeal.
Speaking at a press conference at his summer residence in southern France, Macron said he wanted to attend a summit with the leaders of Ukraine, Russia, and Germany - the so-called Normandy format - soon to try and resolve the conflict in which more than 13,000 people have died.
French President Emmanuel Macron told Russian leader Vladimir Putin on Monday that Moscow must abide by fundamental democratic principles, and that it was right to keep a dialogue between the countries to move forward on global crises.
Russian Federation annexed Ukraine's Crimea region in March 2014.
He explained that the discussion of a possibility to hold negotiations in the Normandy format now took place under new circumstances related to the stance of President of Ukraine Volodymyr Zelensky.
"President Zelensky has made offers to which - it seems to us - President Putin should respond in an encouraging way", said a French official, who asked not to be named. Prospects for the resumption of talks are positive given the new Ukrainian President Volodomyr Zelensky is keen on talks and reportedly more flexible than his predecessor. "It's vital that the ceasefire agreed in Sochi is put into practice", Macron told Putin.
"The main public issue will be reviving the Minsk accords", Baunov told AFP.
Moscow has come under frequent criticism from the European Union and other worldwide entities for its involvement in the conflict.
Tensions have shot up since Washington's unilateral pullout from a 2015 deal to rein in Iran's nuclear ambitions, known as the Joint Comprehensive Plan of Action (JCPOA).
Macron also expressed "profound worry" about the bombing by regime forces of Syria's northern region of Idlib, telling Putin that it was "urgent" a ceasefire went into force.
Macron said the situations weren't comparable - but that at least in France, protesters could run for elected office.