Denis MacShane, the UK's former Europe minister, has warned that any "weakening" of the EU after the UK's decision to leave could pose a security threat to the three Baltic states, Latvia, Lithuania and Estonia.
He was responding to a new study by the RAND Corporation, which warned that Russian forces could reach the outskirts of the Estonian and Latvian capitals of Tallinn and Riga, respectively, within 60 hours.
It says a force of about seven brigades, including three heavy armoured brigades, at an annual cost of about €2.4bn, is necessary to repel such a threat.
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The findings are the result of a major study by the organisation, which conducted war games to test Nato's ability to protect the Eastern flank.
MacShane said, "Clearly if the full weight of the Russian military decided to launch an all-out invasion of a Baltic state there is little chance of successfully defeating such an invasion any more than if the US Army to invade and take over a central American state it would be game over in a very short period."
He added, "That is what Nato members have committed to having their own units deployed in the Baltics as well as increasing air patrols. The Baltic states are in Nato and covered by article 5 on mutual defence.
"Vladimir Putin is a Russian nationalist who takes advantage of any breakdown or chaos in one of the former Soviet states but he not an adventurer and is unlikely to seek a full-on confrontation with Nato.
"The greater threat to the Baltic states is any weakening or disintegration of the EU under the pressure from populist nationalist who reject cooperation with Brussels and the EU member states."
A Nato military official said the alliance does not see an imminent threat to any ally, adding, "Nato is a strong deterrent. But over the last couple of years alone, Russia has illegally annexed Crimea and continues its aggressive actions in eastern Ukraine.
"Russian troops remain in Moldova and Georgia, against the will of their governments. Nato has a responsibility to ensure we are ready to defend our allies."
The official added, "That is why we have significantly strengthened the defence and deterrence of allies over the last year. We have visibly increased Nato's presence in the eastern part of our alliance.
"We have increased air and naval patrols, and the number of exercises. We have tripled the size of the Nato response force to more than 40,000 troops and at its core is our very high readiness 'Spearhead Force' or VJTF."
Meanwhile, at the invitation of the Georgian authorities, the North Atlantic Council (NAC), chaired by Nato Secretary General Jens Stoltenberg, will visit Georgia on 7 and 8 September.
Stoltenberg will chair a meeting of the Nato-Georgia Commission in Tbilisi, with the participation of the Prime Minister of Georgia, Giorgi Kvirikashvili.