The shootings took place in Karak, a tourist destination known for one of the biggest Crusader castles in the region, around 120 kilometres south of the capital Amman.
Jordan's general security department said seven policemen, a female Canadian tourist and two Jordanian civilians were killed in a series of shootings.
It said that 27 others, including policemen and civilians, were wounded.
A separate police statement said that "a number of outlaws who committed ugly crimes this afternoon" had been killed and that security forces were combing the Crusader castle for more gunmen.
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"As soon as they reached the area, unknown gunmen who were inside the house opened fire on the patrol, wounding a policeman, and then fled by car," it said in a statement carried by the official Petra news agency.
"Shortly afterwards, gunmen opened fire on another patrol without causing any casualties," it added.
At the same time, gunmen in the Crusader castle opened fire on the Karak police station, "wounding several policemen and passers-by" who were rushed to hospital.
A senior security source said some people were trapped in a lower floor of the citadel when the gunmen took shelter there, but denied media reports that they were being held hostage.
"There are no hostages. But some people who were on a lower floor were afraid of leaving as the gunmen traded fire with the security forces," said the source who did not wish to be identified.
He said that the gunmen were on a higher level inside the fortress.
The general security department statement said "five or six gunmen" were thought to be involved in the shootings.
However, Prime Minister Hani al-Malki, who was addressing parliament at the time of the shootings, said that "special forces and policemen are surrounding 10 gunmen holed up inside the Karak citadel".
It was not immediately clear who was behind the shootings, but Jordan has been hit by Islamist attacks in the past.