On Monday morning the fighting was ongoing, the border guard service said.
Russians made 1.5m trips to Ukraine last year, the country's border guard service said.
Kyrgyz border guards were awaiting a government decision on whether to allow them in, said Gulmira Borubayeva, a spokeswoman for Kyrgyzstan's border guard service.
In June, there were two shootouts between border guards and suspected traffickers here in the Hamadoni border region that left two dead, said Khushnud Rakhmatullayev, the spokesman for the Tajik border guard service.
At first, the case reverberated through the Kazakh border guard service, forcing the resignation of its director and heaping attention on hazing and desertions at the far-flung outposts along Kazakhstan's borders.
The authorities blame a former warlord who became an officer in the Tajik border guard service for recent clashes between his group and government troops that left at least 47 people dead.
Meanwhile in Ukraine's east, the border guard service said a number of its servicemen had been injured in an attack by around 100 armed insurgents on their camp in Luhansk, a major eastern Ukrainian city near the Russian border.
In 2003, on Putin's order, the FSB absorbed the border guard service and assumed some of the powers of the former Federal Agency for Government Communications and Information, or FAPSI, which handles electronic eavesdropping.
However, Ukraine's border guard service said its personnel at the Izvaryne post, Luhansk region, were forced to retreat into Russian territory.
A spokesman for Russia's border guard service was also quoted by Russian news agencies as denying that any Russian military units had entered Ukraine.
