Speaking in London ahead of a major Nato summit in Wales, the former Danish Prime Minister pointed out that Russia had increased its defence spending by 50 percent since 2008, while spending by Nato countries had fallen by 20 percent.
"It’s time to stop the defence cuts, to start reversing the trend, and to gradually increase our defence spending as our economies recover," Rasmussen said.
Stoltenberg, who is set to take over from Rasmussen on 1 October, will meet the current Nato head in Brussels early next week for a thorough briefing on the organisation's priorities.
Rasmussen said in London that the burden of the increased spending would need to come from European countries as the United States already contributes two-thirds of Nato spending.
"Many of the major capabilities we need are provided solely by America, and quite simply, this is unsustainable," he said. "If we Europeans want the United States to remain committed to European security, we must show a commitment to pick up our part of the bill."
If all Nato members spent 2 percent of their GDP on defence, as they are encouraged to do under the agreement, the alliance would have an addition $90bn of spending power, he said.