The demands came as police said that six victims had been killed in the attack along with the perpetrators of the outrage.
After last month's attack at the Manchester Arena, which claimed 22 lives, campaigning was suspended for several days.
The call for political activity to be put on hold was made by Mark Oxley in a petition he posted on the Change.org website.
"I and I'm quite sure a high percentage of the UK population agree that now is not the time to have a general election, after a second devastating attack I believe it is time to prioritise the safety of our country and its people, that's why I ask you to call off the general election for the foreseeable future." he wrote.
His views were shared by many on Twitter.
One user, called Matt, said he genuinely felt it was no longer safe to press ahead with the poll.
Others supporting a suspension included the actress and activist, Anna Friel, who said the election should be delayed.
Chris Cook argued that it was impossible to have an election at a time when the news agenda was being dominated by terrorism.
Another Twitter user, Ben Dean, said that if campaigning had to be suspended a strong leader would postpone the election.
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