The Western Australian MP told SBS that Tony Abbott should step down and the leadership spilled.
Mr Jensen said the government's position was "untenable".
"What we are looking at in effect is tactics and tactical policy, the minutia rather than the bigger picture,” he said.
“I don’t the Prime Minister sees that and actually understands that nature of the program.”
Listen: Dennis Jensen speaks to Stephanie Anderson.
Mr Jensen, who was elected in 2004, is the first Liberal MP to go on the record calling for Mr Abbott to step down.
He said Mr Abbott was informed of his position on January 23, but he won't call for a spill.
"I don’t want to just become an assassin," he said.
"However I believe that change in the leadership is necessary."
Mr Jensen said he hoped for a change in leadership by next week.
"I'd prefer whatever happens to happen quickly rather than slowly," he said.
"We can't just keep on like this."
Former Liberal leader Malcolm Turnbull voiced support for Mr Abbott over the weekend, while deputy leader Julie Bishop ruled out , telling cabinet colleagues on Tuesday that she was “not campaigning for the job of Prime Minister”.
“I’m not counting numbers,” she said.
“I will not challenge the leader.”
Earlier on Tuesday, Liberal MP Andrew Nikolic urged his colleagues to 'knuckle down' amid leadership speculation for fear of being tarred with the same brush as the Rudd-Gillard Government.
In an email sent to colleagues, Mr Nikolic said he wrote “” in the wake of Mr Abbott's decision to nominate Prince Philip for a knighthood.
“In recent days, media reports suggest we are showing signs of the same sort of ill-disciplined introspection that characterised the Rudd-Gillard-Greens Coalition - the very same behaviours that the Australian people comprehensively rejected in September 2013,” he said.
“Recall for a moment how absolutely fed up with your constituents were with government that focused on itself rather than the needs of our communities.
“My electorate still feels like that and I hate the thought they might tar us with the same brush.”