[I]n 1976, the lives of Mitt Romney and Benjamin Netanyahu intersected, briefly but indelibly, in the 16th-floor offices of the Boston Consulting Group, where both had been recruited as corporate advisers. At the most formative time of their careers, they sized each other up during the firm’s weekly brainstorming sessions, absorbing the same profoundly analytical view of the world.

That shared experience decades ago led to a warm friendship, little known to outsiders, that is now rich with political intrigue. Mr. Netanyahu, the prime minister of Israel, is making the case for military action against Iran as Mr. Romney, the likely Republican presidential nominee, is attacking the Obama administration for not supporting Mr. Netanyahu more robustly.

The relationship between Mr. Netanyahu and Mr. Romney — nurtured over meals in Boston, New York and Jerusalem, strengthened by a network of mutual friends and heightened by their conservative ideologies — has resulted in an unusually frank exchange of advice and insights on topics like politics, economics and the Middle East.

When Mr. Romney was the governor of Massachusetts, Mr. Netanyahu offered him firsthand pointers on how to shrink the size of government. When Mr. Netanyahu wanted to encourage pension funds to divest from businesses tied to Iran, Mr. Romney counseled him on which American officials to meet with. And when Mr. Romney first ran for president, Mr. Netanyahu presciently asked him whether he thought Newt Gingrich would ever jump into the race.

Only a few weeks ago, on Super Tuesday, Mr. Netanyahu delivered a personal briefing by telephone to Mr. Romney about the situation in Iran.

“We can almost speak in shorthand,” Mr. Romney said in an interview. “We share common experiences and have a perspective and underpinning which is similar.”