With the new threats posed by Isis and Russia, the agenda at this week's Nato summit is full to bursting

The last time the UK hosted a Nato summit was in 1990, when Margaret Thatcher was prime minister, the cold war was coming to an end, and the alliance was questioning its relevance in a multipolar world where soft power might count more than hard power. The old chestnut about Nato's purpose voiced by the first Nato secretary general, Lord Ismay – "to keep the Russians out, the Americans in" – looked hopelessly anachronistic. Russia famously had become a country with which the west felt it could do business.

A quarter of a century later, Putin's actions, and the ever more grisly new threats posed by Islamic militants, has given Nato a new lease of life. Indeed, Nato is now so relevant that David Cameron's chief task as host to this week's summit in Wales has been to ensure that the agenda does not burst at the seams. Discussions will range across the Russian advance in Ukraine and expansionist threat to the Baltics, the Nato withdrawal from Afghanistan next year, the possibility of wider alliance air strikes in northern Iraq against Islamic State (Isis), the need for Nato to produce a viable rapid reaction force in Europe as well as respond to the threats of hybrid warfare and terrorism.

Cameron has ensured that the crisis posed by Isis – made even more pertinent by the latest beheading and the threat to a British citizen – will be discussed both at a working dinner on Thursdaytomorrow evening, and then again on Friday as the 28 members discuss asymmetric warfare, and how to respond to threat of terrorism.

No 10 is hoping that dinner discussions, or in the margins, will reveal more about Barack Obama's thinking on how to combat Isis not just in Iraq, but also in Syria. Cameron has said that he supports the current round of US air strikes – now numbering over 130 – and "will continue to keep asking the question of how can we in Britain best pursue our national interests and help those people on the ground who are doing most to combat Isis". No 10 is confident that it has the legal grounds for participation in air strikes, or the facilitation of US air strikes, but is wary of the wider politics.

Last summer Cameron set a red line in the wake of Bashar al-Assad's chemical attacks in Syria and had to watch as his fellow MPs turned that line to dust, leaving him furious and looking foolish. It is a democratic decision that still defines UK foreign and defence policy.

Privately, Cameron is still waiting to hear more clearly from the hesitant Obama about what his strategic thinking might be. Indeed some around the prime minister lose patience with the president's methodical caution, even if they accept there are no easy options.

It was not expected – at least before today's grisly events – that Obama would make a request for a bombing campaign extending into Syria. America has insufficient intelligence on Isis forces inside Syria, and on the impact of any attacks on further western hostages held by Isis. Nato members also need to gauge the wisdom of being seen to be bombing President Assad's enemies.

But if Cameron has his occasional moment of impatience with Obama, he has lost all remaining illusions about Vladimir Putin, a man that at one point he believed he had developed a frank and valuable dialogue.

Thus, this week he effectively called Putin a liar, saying: "The evidence was overwhelming that Russian troops with Russian equipment are on Ukraine's soil."

For all his rhetoric about Munich 1938 and the need to avoid appeasement, Cameron's emphasis in the Ukraine is economic, not military, saying he has been "at the absolute front end of those arguing for broader sanctions". His latest target as part of the European Union's level-three sanctions is a boycott of Russia's syndicated loan market, worth more than $45bn in business.

He insists that economic sanctions are working, with Russia now in negative growth, and says Russia needs America and Europe more than America and Europe need Russia. "We need to make that relationship pay and play," he says. But Cameron, in an act of political solidarity, has invited Ukraine's president, Petro Poroshenko, to the summit, and the British announced yesterday it will send troops to the Ukraine, a non-Nato member, in the next month to take part in possible military exercises.

Even if Ukraine isn't a Nato member state, such exercises would still send a signal of sorts to Moscow. But both Germany and Britain have rejected sending arms to the Ukrainian government, or sending vessels to the Black sea to deter further Russian attacks.

Cameron is also determined to ensure the summit makes clear that Nato is "utterly resolved" to block any Russian attempt to repeat its destabilisation tactics in the Baltic states of Estonia, Latvia and Lithuania – all members of Nato and the EU.

Although small in absolute terms, the three Baltic states contribute greatly to Nato in relative terms. Estonia is the regional leader in defence matters and is currently one of only four Nato countries that spend the required 2% of gross domestic product on defence as recommended by Nato. All three countries sent troops to Iraq and have troops fighting in Afghanistan. Estonian troops are serving in Helmand province in southern Afghanistan, one of the most dangerous areas in the country.

A clear signal will be sent. Cameron promises that Nato is deadly serious about its obligations to mutual self-defence for Nato members under Article 5, including by pre-positioning Nato troops.

"It is very important when Russians looks at countries like Estonia or Latvia or Poland that they don't just see Estonian, Latvian and Polish soldiers – they see French, German, British soldiers too," he said.