Jalili is considered to be close to supreme leader Ayatollah Ali Khamenei, who has the final say on Iran's nuclear programme, which Western powers fear is aimed at producing atomic weapons.
Leading Iran's nuclear negotiating team, he also represents Khamenei in talks with the P5+1 countries -- the US, Britain, France, China, Russia and Germany.
Today's live debate, the last of three before the June 14 election, focused on foreign policy, with the nuclear issue stealing the spotlight.
"If it was not flawed, we would not be in this situation," he said referring to tough sanctions imposed by the United States, the European Union and the United Nations Security Council.
Velayati, who was Iran's top diplomat for 16 years before being made foreign affairs adviser to Khamenei, said the approach had brought unnecessarily damaging sanctions on Iran.
"Diplomacy is not only roughness and hardiness. It is bargaining," he said.
"The art of diplomacy is that we save the nuclear right, while at the same time, we reduce the sanctions."
Iran's currency, the rial, has also lost more than two-thirds of its value since early 2012.
Jalili's negotiating style was also criticised by another candidate, Hassan Rowhani, who headed a relatively moderate nuclear negotiating team under reformist president Mohammad Khatami in the early 2000s.
"Those with experience who can negotiate with logic should be put in charge" of the nuclear case, Rowhani said.
His call was echoed by conservative hopeful Mohsen Rezai, ex-commander of the Revolutionary Guards, who urged immediate results in talks with world powers.
Parallel to diplomatic efforts by world powers to end the standoff with Iran, the UN's atomic watchdog is investigating Tehran for its past nuclear activities, which the Vienna-based body says might have been aimed at "possible nuclear weapons development."
Iran denies claims its nuclear programme is aimed at developing weapons, and insists it is peaceful.
