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.
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.”
Read more on http://www.bbc.com/news/election-us-2016-37966027