The five three-year contracts up for grabs cover France, the UK, Italy, North America and the combined market of Germany, Austria and Switzerland. A further lot for the Republic of Ireland will be issued separately at a later date.
The re-pitch process has been trigged by EU procurement rules requiring regular reviews of public bodies' supplier relationships.
The UK brief for Malta's tourism PR is currently held by Brighter Group.
The Malta Tourism Authority says that the World Economic Forum rates the small Mediterranean archipelago as the number one in the world for prioritisation of the tourism industry. It reported an increase of nearly a fifth in the number of visitors in June this year versus the same month last year, reaching 232,000. Tourist figures increased 10 per cent between 2015 and 2016.
The authority is asking for submissions via its website by 26 September.