The commission said it was reviewing bids by Russian nuclear company Atomstroyexport and a French-Japanese consortium known as ATMEA.
"While there remains significant work yet to be done with respect the project, JAEC is proud of the progress made thus far, which marks a significant milestone for ... Jordan in its pursuit of a safe, secure, reliable and economically competitive energy source," JAEC Chairman Khaled Touqan was quoted by Jordan's news agency Petra as saying.
JAEC said that Jordan faces a "tremendous" energy supply challenge, which convinced the Jordanian government to investigate the potential of nuclear power.
An early April attack on a natural gas pipeline in the Sinai Peninsula in Egypt disrupted gas supplies to Israel and Jordan for the 14th time since the Egyptian revolution in early 2011.
The Jordanian government is said to be examining the possibility of getting natural gas from Persian Gulf states or tap into liquefied natural gas from its neighbors, while Israel is examining natural gas supplies in the Mediterranean Sea.