The resignation of Alan Duncan, a junior foreign office minister who has long been critical of Johnson, underlines the strength of feeling in the governing Conservative Party and parliament against a no-deal Brexit which many businesses say would be catastrophic for the economy.
His move follows last week's resignation of Margot James, a culture minister when she described Johnson's do-or-die promise to leave the EU by Oct. 31 with, or without, a deal as "quite incredible" for going against business organizations.
On Sunday, Finance Minister Philip Hammond also said he would resign rather than be sacked by Johnson, promising to fight with others in parliament to stop a no-deal Brexit.
A Foreign Office spokeswoman confirmed that Duncan had resigned.
If the polls and bookmakers are right, Johnson will become Britain's new prime minister on Wednesday and will immediately face the riddle that is Britain's Brexit negotiation.
Johnson, a former London mayor, has said he will ramp up preparations for a no-deal exit to try to force the EU's negotiators to make changes to the agreement that Prime Minister Theresa May sealed and British lawmakers voted down three times.
But opposition in parliament to leaving without a deal is growing and the EU is refusing to budge over the withdrawal agreement.
