But following Iran's development of a nuclear project, several Arab countries have announced their desire to acquire nuclear technology.
"The rules have changed on the nuclear subject throughout the whole region," the Jordanian king said.
"Where I think Jordan was saying, 'we'd like to have a nuclear-free zone in the area,' after this summer, everybody's going for nuclear programs," he added.
Abdullah said any country aquiring nuclear facilities should adhere to international regulations and submit to inspection.
"What's expected from us should be a standard across the board. We want to make sure this is used for energy. What we don't want is an arms race to come out of this," he said.
Shlomo Brom, a researcher at the Institute for National Strategic Studies and former head of strategic planning for the Israeli military, said Abdullah was probably not serious about developing a nuclear programme.
"The Jordanians don't have the resources," Brom said.
Brom said the Jordanian king was probably trying to make the point that if Iran, which is moving ahead with its nuclear programme despite UN-imposed sanctions, is allowed to become a nuclear power, then a regional nuclear race will be unavoidable.
"Abdullah might be saying that if the Iranians aren't prevented from getting a nuclear program, Jordan and everyone else will want one of their own," Brom said.