A cease-fire in eastern Ukraine is set to expire on June 30 amid growing public opposition in Kyiv to an extension of the truce.
On June 29, European Union leaders held talks with the presidents of Russia and Ukraine.
The telephone conference between President Francois Hollande, German Chancellor Angela Merkel, Russia's Vladimir Putin, and Petro Poroshenko of Ukraine lasted more than two hours.
The French presidency said the leaders discussed "the importance of making new concrete advances in the security situation on the ground, prolonging the cease-fire, and putting in place the peace plan" presented by Ukraine.
The Kremlin said the four leaders called on Poroshenko to extend the truce in eastern Ukraine, which is due to end on June 30 at 2200 local time.
A statement from Poroshenko's office said he had called on Putin to strengthen Russian control over its borders to prevent militants and arms entering Ukraine.
It added that Poroshenko will have another phone conference with Putin, Hollande, and Merkel on June 30.
The conversation comes after reports of renewed clashes in eastern Ukraine, where security forces have been battling pro-Russian separatists.
Ukraine's military said five soldiers were killed and at least 17 injured in Donetsk and Luhansk regions at the weekend.
Rebels also seized an air defense unit in Donetsk and took several servicemen prisoner.
Meanwhile, several thousand demonstrators gathered outside the presidential administration building in Kyiv to demand an end to the cease-fire.
Demonstrators say the cease-fire is only giving the rebels time to regroup and rearm.
The protesters demanded that Poroshenko declare martial law in eastern Ukraine, give sufficient weapons to volunteer battalions to fight the "terrorists," and social guarantees for servicemen involved in the army's military operation in the east.
They also called on the president to demand tougher EU sanctions against Russia for supporting the separatists.
Merkel has warned Moscow the EU was prepared for "drastic measures" if no progress was made on Poroshenko’s 15-point peace plan, which involves decentralizing power and holding early local and parliamentary elections.
With reporting by AFP, ITAR-TASS, and Interfax