Russia says Kyiv's forces have fired across the border from eastern Ukraine into Russian territory with assault rifles and grenade launchers.
The Foreign Ministry said in a statement that "we officially demand Kyiv stop firing at the sovereign territory of the Russian Federation."
The Foreign Ministry said Russia's Gukovo border post came under rocket and machine-gun fire on July 29.
Kyiv has previously denied similar charges from Moscow.
Meanwhile, fighting between government forces and pro-Russian separatists has again prevented international investigators from going to the MH17 crash site in eastern Ukraine.
The Dutch Justice Ministry said on July 29 that fighting "on and around the road to the crash site" was keeping a group of Dutch and Australian experts from leaving their base in Donetsk.
Kyiv said on July 28 that its troops had entered a string of towns around the scene of the Malaysian airliner disaster, including Shakhtarsk, which lies 10 kilometers away.
The fighting and explosions had already forced the unarmed mission of Dutch and Australian police to give up their plans to visit the site during the previous two days.
Australian Foreign Minister Julie Bishop called in Kyiv on July 28 for all sides to give inspectors access to the site.
"Our focus is entirely and absolutely on our humanitarian mission," she told reporters. "It has a simple goal: to get on to the crash site as safely as possible and as quickly as possible, do our work in retrieving bodies, remains and belongings, and commits the investigation by presumably taking evidence off the site so it can be examined."
The Malaysia Airlines passenger airplane on a flight from Amsterdam to Kuala Lumpur crashed in eastern Ukraine on July 17, killing all 298 people, mostly Dutch and Australian citizens, onboard.
The West blames pro-Russian separatists for shooting down the plane, while the separatists accuse Kyiv.
Fighting is also reported to be continuing around the city of Donetsk.
The Donetsk city administration said on its website that train departures were suspended after the rail track at several stations was damaged as a result of fighting.
The website said the city's Leninsky and Kyivsky neighborhoods were seriously damaged by artillery fire.
So far, there have been no reports of civilian deaths and injuries in the most recent combat.
Around the eastern city of Luhansk, Ukrainian authorities said militiamen are continuing to attack army-held areas around the airport with artillery and missile fire.
Kyiv announced on July 29 that to date a total of 1,236 servicemen had been wounded since the military operations in eastern Ukraine started.
Ukrainian Defense Ministry military and medical department director Vitaliy Andronatyy said that among the wounded, 745 are in hospitals and 36 suffered severe injuries.
Separately, Russia said on July 29 that the latest UN human rights report on fighting between Ukrainian forces and pro-Russian separatists in eastern Ukraine was "hypocritical."
The Russian Foreign Ministry said the report had failed to mention the detentions of Russian journalists in eastern Ukraine and the reported use of heavy rockets by the Ukrainian Army against civilians.
The UN human rights office on July 28 accused pro-Russian separatists of subjecting eastern Ukraine to "a reign of intimidation and terror."
UN High Commissioner for Human Rights Navi Pillay also said the downing of the Malaysian airliner "may amount to a war crime."
With reporting from Interfax and AFP