Nato has drawn up plans to strengthen military co-operation with the former Soviet states on Russia's southern flank after the Kremlin's seizure of Ukraine's Black Sea peninsula of Crimea.

Nato foreign ministers were meeting in Brussels on Tuesday to discuss the alliance's response to the Ukraine crisis amid continued fears of Russia's territorial ambitions and what the Americans term a "tremendous" buildup of Russian forces on Ukraine's eastern border.

Before the meeting, a Nato committee drafted plans "for promoting stability in eastern Europe in the current context" by increasing military co-operation with Armenia, Azerbaijan, and Moldova – all in Russia's "near abroad" and considered by Moscow as falling within its sphere of influence.

A confidential seven-page paper leaked to the German news weekly Der Spiegel proposed joint exercises and training between Nato and the three countries, increasing the "interoperability" of their militaries with Nato, and their participation in Nato "smart defence" operations.

The paper also proposed opening a Nato liaison office in Moldova, military training for Armenia, and projects in Azerbaijan aimed at securing its Caspian Sea oil and gas fields.

Nato and EU member states such as Poland and the three Baltic countries (Estonia, Latvia and Lithuania) are alarmed at Vladimir Putin's expansionist policies. There are widespread suspicions that the Kremlin will seek to destabilise and coerce Moldova ahead of its scheduled signing of a trade and political pact with the EU in June.

A woman walks past a train loaded with Ukrainian tanks that are set to leave the Crimean peninsular. Photograph: Max Vetrov/AFP

The US has responded to the pleas from eastern Europe by reinforcing Nato air patrols over the Baltic and dispatching aircraft to Poland. The foreign ministers are expected to discuss how to contribute to the precautionary moves, with Britain, Denmark and Germany offering to supply more air power.

"We should do everything we can to reassure our friends and colleagues in Latvia, Lithuania and Estonia and in Poland that we really believe in their Nato membership and the guarantees that we have given them," the British prime minister, David Cameron, said.

Training for Ukrainian forces and freezing of military co-operation with Moscow were also to be discussed.

According to Germany, Putin told the chancellor, Angela Merkel, he was pulling back some of his forces from the Ukrainian border. But he is believed to have moved just 500, out of tens of thousands.

Nato's supreme commander in Europe, the US general Philip Breedlove, warned at the weekend that the Russian buildup was "very, very sizeable and very, very ready". He said the Kremlin could move to seize Transnistria, a Russian-speaking part of Moldova that has been locked in a "frozen conflict" and effectively controlled by Russia since the 1991 collapse of the Soviet Union.

Britain's defence secretary, Philip Hammond, said the UK was considering increasing its participation in Nato military exercises in eastern Europe.

"Certainly one of the things we are looking at is a greater participation in exercises in the Baltic states, the eastern European Nato member countries, as a way of reassuring them about our commitment to article five of the Washington treaty, the mutual guarantee," Hammond told the BBC.

Article five is the "all for one, one for all" pledge that obliges Nato to come to the military rescue of any member state that is attacked.

While Barack Obama has declared that Nato must respond to the Russian force with "strength and conviction", there is a sense among Nato diplomats that the Kremlin's strategy has reinforced Nato's raison d'être, boosting the arguments for its continued existence against regular calls for its dissolution as a cold war relic.

A Nato spokesman said the meeting would "focus on increasing support for Ukraine and on the consequences of Russia's illegal military actions against Ukraine for Nato-Russia relations".

While the meeting is to focus on boosting security in eastern Europe, there have also been calls to establish Nato bases in the countries of the former Soviet bloc. Nato avoided such moves during the alliance's expansion to eastern Europe in the 1990s for fear of antagonising Russia. The topic is still controversial and would be likely to run into resistance, especially in Germany and elsewhere in western Europe.