The Taliban, fighting to reimpose strict Islamic law after their 2001 ouster, took control of another city in northern Afghanistan on Wednesday, an official said, the eighth provincial capital to fall to the insurgents in six days.
They control much of the country's northern provinces adjacent to ex-Soviet Central Asia. An EU official said on Tuesday the militants now control 65% of Afghanistan.
Shoigu said the Taliban has promised not to cross the border, but that Moscow would continue holding joint drills with its allies in the region.
Russia operates a military base in Tajikistan and the former Soviet republic is a member of a Moscow-led military bloc, meaning that Moscow would be obliged to protect it in the event of invasion. Uzbekistan also has close ties with Russia.
Russia held drills with Uzbekistan and Tajikistan near the Afghan border this month. Russia has also reinforced its military base in Tajikistan with new armored vehicles and firearms.
The Soviet Union occupied Afghanistan from 1979 to 1989, leaving after 15,000 of its troops were killed and tens of thousands were wounded.