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
Bells in Liverpool tolled 96 times as the city remembered those who died 26 years ago in the Hillsborough disaster.