Ukrainian President Petro Poroshenko urged President Vladimir Putin to strengthen Russian control over its borders to prevent militants and arms entering Ukraine after violence broke a truce there in a two-hour phone call on Sunday.
The cease-fire, declared by Poroshenko on June 20 to allow for peace talks with the pro-Russian rebels, is due to expire at 1900 GMT on Monday, a deadline also set by EU leaders considering new sanctions against Russia.
The cease-fire has been shaky since it started, with each side accusing the other of numerous violations.
A statement issued by Poroshenko's office said he underlined Ukraine's willingness to maintain the cease-fire at least until Monday evening, but expressed concern about the situation, noting what he said were multiple violations of the truce by separatist fighters.
He called on Putin to strengthen border controls from the Russian side to stop what Ukraine says is the flow of weapons, fighters and mercenaries.
The statement came after a four-way telephone conversation among the Ukrainian and Russian leaders, French President Francois Hollande and German Chancellor Angela Merkel.
Merkel and Hollande encouraged the Ukrainian and Russian presidents to work on meeting the EU conditions, Hollande's office said in a statement.
The EU's demands included the return of three border checkpoints to Ukrainian control, verification of the cease-fire by monitors from the Organization for Security and Cooperation in Europe, and talks to put Poroshenko's peace plan in place.
The four leaders agreed to speak again on Monday, the statement added.
The Kremlin's account of the conversation made no mention of the European conditions and stressed the joint call on Poroshenko not to resume his eastern campaign.
It also once again urged Ukraine to accept "immediate" Russian humanitarian aid in the conflict zone. Kyiv suspects Moscow of planning to use such deliveries to smuggle arms to the rebel fighters.
The four-way phone call was the latest in a series of discussions the four leaders have held in recent weeks in an effort to stop the fighting that has killed more than 400 people since April.
The European Union has threatened more penalties on Moscow beyond existing asset freezes and visa bans unless pro-Russian rebels act to ease the crisis in eastern Ukraine by Monday.
The United States has promised to move in lockstep with Europe on Russian sanctions in the Cold War-style confrontation over the future of the strategic ex-Soviet state.
Russia's economy minister warned on Saturday that new sanctions could "seriously" impact growth that the International Monetary Fund believes may only reach 0.2 percent this year.
But public statements in Moscow indicate it is busy preparing an economic counter-offensive that would put up prohibitive barriers to Ukrainian trade.
Foreign Minister Sergey Lavrov said on Saturday that Russia would treat Ukraine and the ex-Soviet states of Georgia of Moldova that signed their own EU deals on Friday "based on one criterium -- how (the agreements) might hurt Russian trade."
Russian and EU ministers have tentatively agreed to meet on July 11 to discuss how Moscow's concerns might be best addressed.
Violence near Slovyansk
Ukraine's National Guard said on Sunday rebels had used tanks and mortar shells to fire on a checkpoint near the separatist stronghold of Slovyansk, about 100 kilometers (60 miles) from the border with Russia.
“There were no casualties among the military personnel there,” its statement said. A spokesman for the operation told Channel 5 television that five soldiers had been killed in the past few days by rebel violence in violation of the truce.
Interfax news agency cited rebels as saying Ukrainian forces had shelled around Slovyansk, hitting a marketplace and an apartment building, causing injuries.
Poroshenko, under pressure from the West to keep up the cease-fire during talks with the rebels, is facing rising anger over the truce, which some Ukrainians say is only giving the rebels time to regroup and rearm.
Poroshenko, who accuses Moscow of fanning the violence in eastern Ukraine, on Friday extended the cease-fire until 10 p.m. (1900 gmt) on Monday, hours after returning from a summit in Brussels with EU leaders where he signed a landmark economic integration pact with Europe.
The truce, his website said, was extended in line with a Monday deadline set by EU leaders for the rebels to agree to cease-fire verification arrangements, return border checkpoints to Kyiv authorities and free hostages including detained monitors of the OSCE rights and security watchdog.
Pro-Russian separatists released four OSCE monitors late Saturday, the second of two groups detained last month.
Moscow denies helping the insurgents and says it is the pro-Western Ukrainian government that is fanning the violence.
Talks are meant to include separatists in Ukraine's Donetsk and Luhansk provinces, Ukrainian ex-president Leonid Kuchma as Kyiv's representative, Moscow's ambassador to Kyiv and members of the OSCE.
But persisting violence has increased political pressure on Poroshenko, who promised to end the crisis in the east in a matter of weeks, to step up what he calls an anti-terrorism operation against the rebels.
Hundreds of people rallied in central Kyiv on Sunday for Poroshenko to call an end to the cease-fire and boost operations in the two provinces, where separatists have seized state buildings and weapons arsenals.
Some information for this report provided by Reuters, AFP and AP.