Jordan's Public Security Directorate referred to those being targeted in the raids as "outlaws" but did not elaborate.
The directorate reported there were deaths among the gunmen but did not say how many, and that three members of the security forces were hurt.
The statement said clashes began earlier yesterday and continued in the evening. The daily al-Ghad said more than 20 suspected militants were arrested in the operation.
Amateur video posted online showed groups of men, apparently onlookers, standing in a street as heavy gunfire could be heard in the distance. Since last year, Jordan assumed a high-profile role in the US-led military campaign against the extremist Islamic State group which controls large areas of neighbouring Iraq) and Syria.
Jordan has also cracked down domestically, with IS sympathisers, including those expressing support for the group in social media, facing several years n prison.