* Says militants and weapons entering Ukraine from Russia
* Fighting flares around flashpoint city in east Ukraine
* Violence strains ceasefire due to expire on Monday (Adds statement from Poroshenko)
By Thomas Grove
KIEV, June 29 (Reuters) - Ukrainian President Petro Poroshenko urged President Vladimir Putin on Sunday to strengthen Russian control over its borders to prevent militants and arms entering Ukraine after violence broke a truce there.
The ceasefire, declared by Poroshenko on June 20 to allow for peace talks with the pro-Russian rebels, is due to expire on Monday, a deadline also set by EU leaders considering new sanctions against Russia.
The statement came after a four-way telephone conversation among the Ukrainian and Russian leaders, French President Francois Hollande and German Chancellor Angela Merkel, said a statement from Poroshenko's office.
"Ukraine called on the President of Russia to strengthen control over the Russian side of the state border in order to stop the penetration into Ukraine of militants and mercenaries and supplies of weapons and armoured vehicles," it said.
The four leaders agreed to speak again on Monday, the statement added.
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.
Ukraine's National Guard said on Sunday rebels had used tanks and mortar shells to fire on a checkpoint near the separatist stronghold of Slaviansk, about 100 km (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 Slaviansk, hitting a marketplace and an apartment building, causing injuries.
Poroshenko, under pressure from the West to keep up the ceasefire 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 ceasefire 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 ceasefire verification arrangements, return border checkpoints to Kiev authorities and free hostages including detained monitors of the OSCE rights and security watchdog.
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 Kiev's representative, Moscow's ambassador to Kiev 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 Kiev on Sunday for Poroshenko to call an end to the ceasefire and boost operations in the two provinces, where separatists have seized state buildings and weapons arsenals.
"Not only do I support the operation, I want martial law set up in two provinces that will finally give us the ability we need to fight this Russian intervention," said former soldier Viktor Kamenev, 66.
"You can't talk to terrorists, you can only use the language of force," he said.
Pro-Russian separatists released four OSCE monitors on Saturday, the second of two groups detained last month.
EU leaders said on Friday they were ready to meet again at any time to adopt more sanctions on Russia. Diplomats said they could target new people and companies with asset freezes as early as next week. More than 60 names are already on the list.
Although it has drawn up a list of hard-hitting economic sanctions, the EU is still hesitating over deploying them because of fears among some member states of antagonising their major energy supplier.
German Chancellor Angela Merkel said on Friday the EU expected progress within hours.
"If we don't see any steps forward on any of the points, then we are also prepared to take drastic measures," she said. (Writing by Thomas Grove; Editing by Richard Balmforth and Tom Heneghan)