Barack Obama leaves Washington on Tuesday for the small Baltic state of Estonia on Russia's north-western border to reassure the vulnerable country that it is safe within Nato from Vladimir Putin's clutches.

En route to Wales for a Nato summit that Putin, in Ukraine, has transformed into the most important such gathering since the end of the cold war, Obama will reiterate the alliance's '"all-for-one and one-for-all" defence pledges of Nato's article five commitments, seeking to assuage Estonian, Latvian, Lithuanian, Polish and Romanian fears of revisionist Kremlin regional ambitions.

Putin's campaign in Ukraine, his seizure of Crimea and his invasion of eastern the country have the Baltic states and Poland in told-you-so mood. They have been clamouring for years for greater commitments from the west and voicing their suspicions of Russia. Ukraine has vindicated their angst, but generated an ambivalent response in the rest of Europe, including in the east where the Czechs, Slovaks, and Hungarians are much more inclined to give Putin the benefit of the doubt.

About one in four Estonians are ethnic Russians or native Russian-speakers, a bigger proportion than in Ukraine, where Putin justified his actions by referring to the defence of Russophones and ethnic Russians. Latvia, where about 30% are ethnic Russians, feels similarly exposed to Putin's summoning of Russian nationalism.

Anders Fogh Rasmussen, secretary general of Nato, told the Guardian last week: "Obviously some of our member states are very concerned that the Russians say they reserve their right to intervene in other countries if they consider it necessary to protect the interests of Russian-speaking populations in other countries. Obviously, that creates a lot of concern among the allies."

But it is in the south, not in the north-west, that the chilly blast of Putin's rhetoric is being felt, far away from Europe and from Nato.

In little-noticed remarks last week, he called into question the legitimacy of the post-Soviet state of Kazakhstan while ordering the Kazakhs to be on their best behaviour when it came to serving Russian interests.

The remarks, to an audience of young people in Russia on Friday, sent shocke waves through the central Asian republic, which also hosts a large ethnic Russian minority centred in the north on the Russian border.

Putin said there had never been a country called Kazakhstan, that the republic was purely the product of the current president, Nursultan Nazarbayev.

"I am confident that a majority of its population supports development of close ties with Russia," said Putin. "Nazarbayev is a prudent leader, even the most prudent in the post-Soviet space. He would never act against the will of his country's people."

Kazakhstan, he said, was "part of the large Russian world that is part of the global civilisation in terms of industry and advanced technologies. I am confident that that's the way things are going to be in the medium – and long-term."

Nazarbayev had "done a unique thing. He created a state in a territory that had never had a state before. The Kazakhs had no statehood."

When the Soviet Union disintegrated in 1991, it left 25 million Russians in new countries on Russia's rim, – what Moscow calls the "near abroad". Putin, who has called the USSR's collapse the 20th century's greatest tragedy, although it was seen in most of the "captive" countries as a liberation, has played the ethnic card to stir up trouble, justified his actions in the name of the defence of Russians, and generally displayed a proprietorial attitude towards Russia's neighbours, using trade and energy as weapons to get them to toe the line.

Ukraine is his third war in the post-Soviet space. He crushed the Chechen rebellion. He invaded Georgia and still controls two chunks of it. He now controls tracts of Ukraine. Russia has long held on to the Transnistria slice of Moldova.

Nazarbayev was unimpressed by Putin's views on Kazakh statehood and threatened to loosen ties with Russia, which could provoke a forceful Kremlin reaction.

"Our independence is our dearest treasure, which our grandfathers fought for," Nazarbayev said. "First of all, we will never surrender it to someone, and secondly, we will do our best to protect it … Kazakhstan will not be part of organisations that pose a threat to our independence."

Unlike Ukraine and Kazakhstan, the Baltic states are members of both the European Union and Nato.

Rasmussen insisted that any attack on a Baltic member state would be met not only with national forces but would be confronted by international Nato forces.

It is unlikely to come to that. But exploiting Estonia or Latvia's ethnic minorities, choking the states by cutting off energy, provocations and destabilisation attempts supported by well-orchestrated propaganda – what Nato officials call "hybrid warfare" after Putin's successful tactics in Ukraine – might leave the west labouring to respond.

Nato alone could not deal with Putin's tactics, Rasmussen admitted.

"You see a sophisticated combination of traditional warfare and disinformation campaigns. This is not only a Nato issue. When it comes to hybrid warfare, we will need more than Nato to counter this."