NATO Secretary General Jens Stoltenberg said on Monday that both the alliance and the EU were stronger with Britain inside, and warned that a "Brexit" could cause instability.

Stoltenberg, the former Norwegian premier who heads the 28-nation military grouping, said that it was "up to the British people" whether they choose to remain in the European Union in a referendum on June 23.

"What really matters for NATO is I strongly believe a strong UK in a strong EU. It is good for both the UK and the EU but also for NATO," Stoltenberg told an event in Brussels held by the Politico Europe newspaper.

"We live at a time of many threats and instability, we don't need more instability, we need more cooperation in Europe."

He added: "It is a great advantage to have the UK being strong in the EU, pushing for security cooperation with NATO... It's good to have the UK in NATO pushing for strategic cooperation with the EU."

Both the EU and NATO have so far largely steered clear of intervening in Britain's increasingly toxic referendum debate, in which Prime Minister David Cameron is pushing for his country to stay in the EU.

Meanwhile Stoltenberg defended NATO after the presumptive Republican US presidential nominee Donald Trump said the alliance was obsolete.

Asked about the comments, Stoltenberg said that "NATO is important for the security of the US and Europe."

He also pointed out that the only time NATO had invoked its collective defence clause since its formation after World War II was "in defence of the United States after the 9/11 terrorist attacks."