MOSCOW — Russia and its allies will have to step up their military activity in the border regions near Afghanistan to prevent militants fanning out from the conflict there to Central Asia and possibly to Syria, President Vladimir V. Putin and senior Russian officials said on Friday, Russian news agencies reported.

“Terrorists of all kinds are gaining influence and do not hide their plans for further expansion,” Mr. Putin told a meeting of the leaders of the Commonwealth of Independent States, a grouping of former Soviet republics, in a resort town in Kazakhstan, in remarks carried on the presidential website. “One of their goals is to break through into the Central Asian region.”

He added, “It is important that we be ready for coordinated action to respond to any such attempts.”

The leaders of the group, composed of former Soviet states, agreed to establish a joint task force to protect their borders against external threats from Afghanistan.

Mr. Putin spoke a day after the White House said it would extend the United States’ military mission in Afghanistan until at least 2017. The Russian government swiftly interpreted the policy shift as an admission of a deteriorating situation in Afghanistan, where the Taliban recently overran the city of Kunduz, before retreating two weeks later.

As envisioned at the meeting on Friday, the new effort would increase the number of border guards and other security officers, as well as forming a rapid-reaction force to respond to any crises on the border with Afghanistan.

In recent days, militant leaders in Syria have issued threats of violence against Russians in retaliation for the bombing campaign Moscow is conducting to aid the forces of President Bashar al-Assad of Syria. Mr. Putin himself acknowledged Friday that as many as 7,000 militants may have migrated from Russia and the former Soviet states to join the Islamic State in Syria.

Among the commonwealth states, Tajikistan, Uzbekistan and Turkmenistan each share a border with Afghanistan.

This would not be the first time that the Kremlin has asserted that the terrorist threat to Central Asia arises from the United States’ actions in Afghanistan. But analysts have often accused Moscow of deliberately exaggerating the threat to justify an expansion of its military and political presence in the region.

On Friday, Russia’s Foreign Ministry denounced Mr. Obama’s decision to halt the scheduled withdrawal of troops from Afghanistan as “another testimony of a complete failure of Washington’s 14-year military campaign.”

Russia has a military base in Tajikistan and an air base in Kyrgyzstan, where the current government closed a United States Air Force base in 2012.

Russia had indicated on Thursday that it was slowing the pace of airstrikes in Syria because the military had concluded the militants were in retreat.

On Friday, Mr. Putin indicated that the pace and duration of the bombing campaign would be determined by the results on the battlefield. “Our operation is limited in time to the Syrian Army’s offensive against terrorists,” he said, without elaborating.