The schoolgirl disappeared after a night out in the Republic of Ireland in 1994 and her body has never been found.
Convicted child killer Robert Howard, who died in prison last year, was the main suspect in her disappearance.
Attempts are to be made to resolve disclosure issues about documents held by the police.
Earlier, lawyers for the Arkinson family asked if there was an "institutional incapability" within the police service (PSNI) to find documents.
A barrister representing the PSNI described the criticism as "tiresome".
The coroner told the court that in anything of this age, nature and complexity there would always be matters which arise which caused pause for thought.
"Thats where we are....it is with a fair wind we will reconvene on the 18th April", he said.
The inquest into the disappearance of Castlederg schoolgirl Arlene Arkinson will not hear any evidence for the next two weeks.