In an opinion piece published in the Washington Post on Thursday in advance of the UN General Assembly annual meeting next week, the centrist cleric said nations needed to seek "win-win outcomes" instead of using "brute force" to combat terrorism, extremism, cybercrime and other challenges.
"Gone is the age of blood feuds," he wrote. "World leaders are expected to lead in turning threats into opportunities."
The piece appeared to be Rouhani's latest signal that he plans to pursue a thaw in relations with the United States and other Western nations, which believe Iran is developing nuclear weapons and have imposed economic sanctions that have damaged Iran's economy.
However, British officials say they would need to be absolutely sure of the safety of diplomats before sending them back to Tehran.
Mark Dubowitz, the executive director of the Foundation for the Defence of the Democracies in Washington, cautioned that Mr Rouhani and Mr Zarif had only limited power in Tehran. The big decisions were made by Ayatollah Ali Khamenei, the Supreme Leader, and the Revolutionary Guard.
"Rouhani and Zarif are the Vice-President for sales and marketing but Ayatollah Khamenei is the chairman of the board while Mohammed Jafari, the head of the Revolutionary Guard, is the CEO, and Qassem Suleimani, the head of expeditionary Quds Force, is COO," said Mr Dubowitz.
The House of Representatives voted 400-20 last month to impose more sanctions on Iran and the Senate is working on its own version of these measures. The legislation could be signed by Mr Obama as early as November.