He said the West faced its greatest security challenge in a generation.
During his election campaign, Mr. Trump described Western military alliance NATO as obsolete.
He suggested that the US would think twice about coming to the aid of any Nato ally under attack if it had not paid its dues.
Writing in Britain’s Observer newspaper, Mr. Stoltenberg conceded that Mr. Trump had a point about the need for some members to make a bigger financial contribution, as the US currently accounted for almost 70 per cent of NATO spending.
But he added that American leaders had always recognised that they had a profound strategic interest in a stable and secure Europe.
“It is all too easy to take the freedoms, security and prosperity we enjoy for granted. In these uncertain times we need strong American leadership, and we need Europeans to shoulder their fair share of the burden,” the former Norwegian Prime Minister wrote.
“Going it alone is not an option, either for Europe or for the United States. We face the greatest challenges to our security in a generation. This is no time to question the value of the partnership between Europe and the United States.”
The 9/11 attack on the US, Mr. Stoltenberg pointed out, was the only time that NATO had invoked its self-defence clause, which requires all members to come to the aid of one that is attacked.
“This was more than just a symbol. NATO went on to take charge of the operation in Afghanistan. Hundreds of thousands of European soldiers have served in Afghanistan since.
“And more than 1,000 have paid the ultimate price in an operation that is a direct response to an attack against the United States.”
The BBC’s Paul Adams in Washington says that what some at the time saw as the musings of a candidate not expected to win are now been seen as posing an almost existential threat to the alliance.
He adds that Mr. Trump’s apparent admiration for Russian President Vladimir Putin sharpens that concern.