They rang during a minute's silence at 15:06 BST, the moment the FA Cup semi-final between Liverpool and Nottingham Forest was halted on 15 April 1989.
Victims' families were joined by supporters and players at a memorial service at Liverpool's Anfield stadium.
Thousands of people sang the club's anthem You'll Never Walk Alone in memory of the 96 fans who died.
Actress and Liverpool fan Sue Johnston read the lyrics of The Beatles song In My Life before embracing Margaret Aspinall and Trevor Hicks, who both lost children at the disaster.
They were recently given CBEs by the Queen for their efforts to secure fresh inquests into the deaths of the 96 Liverpool fans.
Mrs Aspinall, who chairs the Hillsborough Family Support Group, said at the service: "We can't go away from here and see a job part done. We will get it done."
Liverpool captain Steven Gerrard and his Everton counterpart Phil Jagielka also released 96 red balloons at the event.
During the minute's silence, flags on civic buildings flew at half-mast and the Mersey Ferry sounded its horn while barriers at the Mersey tunnels were lowered.
Liverpool Mayor Joe Anderson said: "We will never forget those who died at Hillsborough, and this is a day for us to unite as a city and remember each one and also their families and friends left behind."
Before the service, a Liverpool fan said: "We are a band of brothers - it is sort of a nice thing to come here every year because all of us are mourning altogether, but it is an emotional day too."
The new inquests into the deaths of the 96 Liverpool fans will resume on 20 April at Birchwood Park, Warrington.
They started in March 2014 and are expected to continue until early 2016.
BBC News: Profiles of all those who died

Crews from Tumble and Llandeilo were called to a farm in Maesybont, Llanarthne, at 20:40 GMT on Thursday.
A "Coldcut Cobra" ultra-high pressure water jet, which is on trial with Mid and West Wales Fire and Rescue Service, was used to tackle the blaze.
An environmental protection unit was also sent to reduce the risk of pollution.

The posts will be cut over three years during restructuring after the £11bn merger of Standard Life and Aberdeen Asset Management.
The two companies currently have  a combined worldwide workforce of approximately 9,000 people.
The information is contained in a detailed prospectus published by Standard Life on the deal.
Managers said they expected "natural turnover" to account for some of the reductions, while other steps will be taken to minimise compulsory redundancies.
The merger of Edinburgh-based Standard Life and Aberdeen is aimed at creating cost savings that could add up to £200m per year.
The prospectus for shareholders stated "there will be a need to maximise operational efficiencies and cost synergies" to achieve the expected benefits of the merger.
It continued: "At this time it is estimated that the integration and restructuring will result in a phased reduction of approximately 800 roles from the total global headcount of the combined group as at 31 December 2016 of approximately 9,000 over the three-year integration period.
"Synergies will come in part from employee departures arising from natural turnover.
"Other appropriate steps will be taken to minimise the number of compulsory redundancies, including the active management of Standard Life's and Aberdeen's recruitment and vacancies."
The document reveals that the newly-merged company will be renamed Standard Life Aberdeen plc.
Both companies have agreed on a 16-strong board made up of an equal number of Standard Life and Aberdeen directors.
Standard Life chairman Sir Gerry Grimstone will be the chairman of the newly-merged company while Aberdeen's chairman Simon Troughton will become deputy chairman.
Keith Skeoch, the Standard Life chief executive, and Aberdeen boss Martin Gilbert will become co-chief executives of the new firm.
The two companies agreed the terms of the merger, which will create Britain's biggest asset manager, in March.
Under the terms of the deal, Aberdeen shareholders would own 33.3% and Standard Life shareholders would own 66.7% of the combined group.
A general meeting has been scheduled for June at which shareholders will be asked to approve the merger. If backed, the deal is expected to be closed by mid-August.
Bells in Liverpool tolled 96 times as the city remembered those who died 26 years ago in the Hillsborough disaster.
[NEXT_CONCEPT]
A large timber and tyre fire which burned throughout the night in Carmarthenshire has been extinguished.
[NEXT_CONCEPT]
About 800 jobs are to be cut in a planned merger of two of Scotland's biggest financial companies.