Murray, who quit Labour’s front bench team after Jeremy Corbyn’s election as leader, described the pledge as being a “little bit ridiculous”.
The MP told the BBC’s Sunday Politics Scotland programme his loyalty to the party “should never be in question”.
He stated: “My pledge is every single weekend when I am out knocking on doors, delivering leaflets, staffing street stalls and doing my advice sessions with my constituents, that is my pledge to the Labour Party.
“I think these kind of pledge things are a little bit ridiculous, in my view.
“I won’t be signing it for a number of reasons, firstly because I think it is unnecessary and secondly it asks for a Labour led government – I think we need a Labour majority government.”
Murray, the only Scottish Labour MP to hold on to his constituency when the SNP won all but three seats north of the border in the 2015 Westminster election, added: “I just don’t think we should be signing these pledges, we should be getting on with the task of trying to resolve this Brexit issue, which is number one on the agenda at the moment.”