Ms McLaughlin and her staff were forced to evacuate their office on Thursday afternoon after being informed by police of reports that a bomb was left at the premises.
Police are searching the building.
Said the Foyle MP: “This threat against SDLP Foyle MLA Sinéad McLaughlin is a despicable attempt to intimdate and stop a tireless public representative from doing their job.
“I know Sinéad will not be deterred and my thoughts are with her and her constituency team after what must have been a frightening experience.
“The entire SDLP stands fully behind them in solidarity.
“Elected representatives should be able to go about their duties without having to worry about threats being issued against them.
“We’ve seen recently in England how the targeting of politicians can end up with tragic consequences.
“Sinéad McLaughlin serves the people of Derry and neither she nor her staff should have been subjected to this ordeal.
Said Foyle MLA Sinéad McLaughlin: “This incident has been very upsetting for my staff who come to work every day to help the people of this community with everything from passport applications to PIP appeals.
“Nobody should have to face this kind of threat when simply going about their job.
“While it’s deeply unpleasant to be subjected to this, nothing will stop me from going about my work on behalf of the people of Derry.
“Whether in my career, as a councillor or an MLA I have often faced barriers, but I have always overcome them and it will take more than the efforts of a few idiotic thugs to stop me from working to represent and improve the lives of people here.”