The Foreign Secretary's revelation that the First Minister would receive no help from his department in organising her trip was also dismissed as another "gaffe" which would win support for Scottish independence.
Mr Hunt sparked a diplomatic row after allegedly taking the unusual step of refusing Foreign and Commonwealth Office (FCO) support for Nicola Sturgeon's visit to Belgium because he believed his officials should be "focused on furthering the objectives of Her Majesty's Government".
Ms Sturgeon is due to meet the European Commission president Jean-Claude Junker and the EU's chief Brexit negotiator Michel Barnier today as well as deliver a speech in which she is expected to reiterate her call for Scotland to be an independent country in the EU.
But a spokesman for the First Minister said that while the Foreign Office did provide support for trips to the US or China, visits to Brussels were already handled by Scottish Government staff in Edinburgh and in Belgium.
He said: "The First Minister has already dismissed this as fairly pathetic and childish behaviour.
"Jeremy Hunt is in the middle of a Tory leadership campaign and the Tory leadership contenders appear to be lining up one by one to do our job for us - if it's not Boris Johnson making horrendous gaffes on tax it's Jeremy Hunt saying that Scotland should represent itself internationally.
"If the FCO is refusing to give Scotland the same level of support and representation as it would the rest of the UK then surely it demonstrates stronger than ever why Scotland should be independent."
Asked if Mr Hunt was "blowing hot air", he said: "that is not too inaccurate a summation."
He added: "In terms of the Brussels visit this will have little, if any, affect at all. We have our own office in Brussels which is well staffed and supported and there's little if anything that the FCO would be doing anyway in terms of logistical support.
"Brussels is self-facilitating because we have our own staff, our own presence there, so if's different from other overseas visits where we don't have the same level of staff. Brussels has always been a place where we've been able to do our own thing.
"There's nothing substantially different about this visit in terms of what she's doing, or who she's meeting, to previous meetings. The First Minister has been in Brussels fairly regularly over the last three years - the only thing that's different is there's a Tory leadership contest."
A UK government spokesman had told the Telegraph newspaper: "The UK government's extensive network of diplomatic staff regularly provide support to the UK's devolved administrations for visits relating to areas for which they have a devolved responsibility. However a balance must be struck to avoid supporting activities intended to campaign for policies contrary to HMG's position.
"On this occasion, the Foreign Secretary has requested that the Scottish Government provide its own logistical support for this visit."