The work, for advisory services to the mayor and cabinet members "on developing initiatives, projects and work programmes", is divided into seven lots covering different areas.
Two posts cover media relations, with one position advising on "media management" and the other on "communities’ communication and media" specialising in the BME and Bangladeshi media.
A council spokeswoman said the number of PR roles had not changed and there had always been two, adding that agencies could bid for one or more lots but the last set of posts was held by different individuals and not an agency.
Other lots cover the localism agenda, equalities briefs focusing on women and diverse communities, and roles advising on engaging with young people and the Somali community.
The upper end of the entire contract, including all seven posts, is worth £1.2m if the contract runs for three-and-a-half years.
The initial contract is for 12 months with three potential annual extensions, subject to the availability of funding. The anticipated start date is 12 November 2014.
Lutfur Rahman, the first directly elected mayor in the borough, was re-elected at the 2014 mayoral election in May, after which he became the subject of an investigation into electoral fraud.
He was the subject of a BBC Panorama documentary that alleged he increased funding to Bangladeshi and Somali groups to shore up his vote.
It emerged this month that the mayor spent £128,000 on PR and lawyers to counter the programme. The council was advised by public affairs agency Champollion.
A police investigation into the claims concluded there was no evidence of criminality. DCLG is yet to complete its investigation, and commissioned an audit from PWC of the council finances. Tower Hamlets has applied for a judicial review of the decision to send in the auditor.