Developer Sirius Minerals wants to build the mine near Whitby in the North York Moors National Park.
The MPs, who represent constituencies in the area, said the project would bring "enormous economic benefits".
The intervention comes a week after environmental groups said the plans were a "huge threat" to the area.
The letter comes from Robert Goodwill, the Conservative MP for Scarborough and Whitby, Thirsk and Malton's Conservative MP Kevin Hollinrake and Anna Turley, the Labour MP for Redcar.
The MPs said the project was a "once in a lifetime opportunity".
"A positive decision will bring enormous social and economic benefits to the area by creating jobs, improving training and education opportunities for young people, providing community facilities and by generating more wealth in the economy," the letter said.
Mr Goodwill added the park should not "look a gift horse in the mouth".
Sirius Minerals has previously said the mine would deliver at least 1,000 permanent jobs and would not have a negative impact on the area.
The North York Moors National Park's planning committee meets later to make a decision.
Three MPs have urged members of a national park authority to approve plans for a £1.7bn potash mine when they meet later.