President Barack Obama has said he expects the UK to remain a major contributor to European security and that it will be able to agree an "orderly transition" with the EU.
"I have no doubt that the UK will remain one of Nato's most capable members," he told the FT as alliance leaders gather for a summit.
The meeting will focus on the perceived threat from a resurgent Russia.
But it has been overshadowed by the UK's vote to leave the EU.
Obama warns on Brexit talks
Mr Obama met European Council President Donald Tusk and European Commission President Jean-Claude Juncker on Friday and told a news conference that the Brexit vote had created uncertainty over the future of European integration.
But he rejected as misplaced hyperbole any suggestion that the Brexit vote signified the crumbling of the entire edifice of European security.
While he was confident the EU and UK would work together in a pragmatic fashion, he warned that "no-one has an interest in protracted adversarial negotiations".
"Everybody has an interest in minimising any disruptions as the UK and the EU forge a new relationship," he said.
Nato Secretary General Jens Stoltenberg said he was certain that the UK and the EU would find a way to co-operate and that the UK would remain a strong and committed ally in Nato.
Prime Minister David Cameron was later expected to underline the UK's commitment to Nato in the wake of the UK referendum, with a commitment to meeting the alliance's target of spending 2% of GDP on defence.
Nato will agree on Friday to bolster the Western military alliance's defences next year with four multinational battalions in Estonia, Latvia, Lithuania and Poland made up of some 3,000 troops from the UK, US, Germany, and Canada. Nato members made the decision after Russia's annexation of Crimea from Ukraine in 2014.
A 500-strong UK battalion will be deployed to Estonia and 150 UK troops will be based in Poland. UK Defence Secretary Michael Fallon said the aim was to "deter Russia from any further aggression".
In 2017, the UK will also take over the running of a standby Nato force, with 3,000 troops based in the UK and Germany.
"Nato does not seek confrontation," Mr Stoltenberg said in an address on Friday, vowing continued dialogue with Russia. "We don't want a new Cold War. The Cold War is history and it should remain history."
However, Russia's ambassador to Nato, Alexander Grushko, warned of a risk of a "spiral of confrontation", by building a "new Iron Curtain". Mr Grushko told the BBC that the decision would lead to "military consequences".
Tensions between the Atlantic alliance and Moscow are growing again. Russia's seizure of the Crimean peninsula from Ukraine and the involvement of its troops in the fighting in eastern Ukraine has, in Nato's view, "torn up the rule-book" for the way security matters are dealt with in the post-Cold War world.
Writing in the Financial Times, President Obama said Nato and the EU should "deepen security co-operation" and agree that sanctions on Russia should remain in place until the Kremlin fully implemented the Minsk agreement on halting the fighting in eastern Ukraine.
The EU and Nato signed a joint declaration on Friday agreeing to "accelerated practical co-operation" in the face of so-called hybrid threats as well as in maritime and cyber security and joint exercises.
Donald Tusk said that sometimes it appeared that the EU and Nato were on "two different planets", and it made sense to work more closely together.
"At stake is real life," he said. "Our critical infrastructure could be attacked, our banking system could be hacked or our citizens could be exposed to disinformation campaigns via social networks."
In words echoed by Mr Stoltenberg in Warsaw, President Obama wrote in his FT article that Article Five of the North Atlantic Treaty, in which an attack against one Nato member is considered as an attack against all, should be reaffirmed.
German Foreign Minister Frank-Walter Steinmeier last month urged Nato not to inflame tensions by "creating pretexts" and "sabre-rattling and warmongering".
However his remarks have been criticised by cabinet colleagues, and by ex-Defence Minister Franz Josef Jung, who pointed out that recent Russian military exercises were far larger than Nato's.