Launched yesterday Telford & Wrekin Council leader Shaun Davies, the aim of the petition is to get the issue discussed in Parliament.
By this afternoon the petition - at petition.parliament.uk/petitions/229602 - had been signed by more than 10,000 people, meaning the government will have to respond. Should the petition get 100,000 signatures then it will be considered for a debate in Parliament.
Russell Griffin spokesman for Telford & Wrekin Council said: "We are absolutely astonished but not surprised in the response from the public to our call for them to sign our petition asking the government to provide a rescue plan to prevent the unavoidable closure of Princess Royal's A&E.
"This clearly shows how important it is to the public and we now call on the government to listen."
News of the petition came as a summit meeting was held on the crisis between Telford MP Lucy Allan, councillors and leaders from Shrewsbury and Telford Hospital Trust (SaTH) including chief executive Simon Wright.
The purpose of the summit was to inform the SaTH board about concerns of residents in Telford and to find out what plans the Trust has to overcome current challenges to keep the A&E open.
Councillor Davies was absent from the meeting, claiming he had been 'uninvited' shortly before it was due to start.
Ms Allan accused him of trying to 'disrupt' the summit and said it was "thought best to ask him not to attend".
She said "he was not prepared to cooperate with the spirit of the meeting".
Councillor Davies said he was excluded after asking for the meeting to be held in public.