Elston was questioned yesterday by members of the Operation Weeting team before being released on bail.
PA editor Jonathan Grun said today: "Laura Elston is a journalist of integrity who has worked for us for over 10 years with great distinction.
"We are offering her our full support and we hope that this matter can be cleared up as quickly as possible."
Elston, 34, joined PA as a graduate trainee in 2000, before being made deputy royal correspondent in 2003 and royal correspondent in 2007.
She was arrested by appointment at a central London police station yesterday afternoon.
Scotland Yard said she was questioned on suspicion of intercepting communications, contrary to Section 1 of the Regulation of Investigatory Powers Act (RIPA) 2000.
Elston is the fifth person to be arrested in connection with the Operation Weeting investigation, which has focused on the News of the World. The other four people who have been detained have all had connections to the newspaper but Elston appears not to.
She is the second person to be arrested within a week in connection with Operation Weeting. Last Thursday a 39-year-old woman was arrested on suspicion of phone hacking and released without charge seven hours after her arrest.
The woman, believed to be freelance journalist and former News of the World contributor Terenia Taras, was bailed to return to a West Yorkshire police station in October, a police spokesperson confirmed.
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