JIRA throws a timeout when trying to import an Execution Results XML and JSON files

When importing an Execution Results XML and JSON files with details of around 800 tests - some of them with requirement links - the following message is displayed on the Import Execution Results dialog:
The call to the JIRA server did not complete within the timeout period. We are unsure of the result of this operation. Close this dialog and press refresh in your browser

After refreshing the page, as instructed, we can verify that the results were successfully imported, but that previous timeout message shouldn't be displayed at all.