Borujerdi's comments came a day after the Security Council overwhelmingly agreed to the new package of economic sanctionstargeting Iran's Revolutionary Guard, ballistic missiles and nuclear-related investments.
Barack Obama, the US president, called the resolution "the toughest sanctions ever faced" by the Iranian government.
"We recognise Iran's rights. But with those rights come responsibilities," he said at the White House.
"And time and again, the Iranian government has failed to meet those responsibilities."
Mahmoud Ahmadinejad, the Iranian president, dismissed the sanctions, calling them valueless.
"These resolutions have absolutely no value for the people of Iran," he said.
"These resolutions are like a used handkerchief for us ... and should be thrown into a waste bin. They cannot hurt Iran."
Later on Thursday, Russia, which voted for more sanctions, said that it would freeze a deal to deliver anti-aircraft missiles to Iran.
"It is compulsory to fulfill a decision by the UN Security Council and Russia is not anexception here," a source in the Federal Service for Military Technical Co-operation, which supervises Russian arms sales, told the Interfax news agency.
There was no official confirmation of the comments.
The new package of sanctions expands an existing arms embargo against Iran, and prevents the country from importing technology for certain kinds of ballistic missiles.
It also imposes an asset ban and a travel freeze on more than three dozen companies and individuals.
Robert Gates tells Al Jazeera's David Frost the vote is to spur Iran nuclear talks
Twelve of the council's 15 members voted on Wednesday to approve the sanctions resolution. Turkey and Brazil both voted against the resolution, while Lebanon abstained.
Recep Tayyip Erdogan, the Turkish prime minister, called the resolution a "mistake" on Thursday, and said both Turkey and Brazil will continue to seek a diplomatic solution to the dispute.
"We would not want to participate in such a mistake because history will not forgive us," Erdogan said.
However, several other European countries praised the sanctions resolution,and the Chinese government endorsed it while insisting that it still wanted a diplomatic solution.
Victor Gao, director at the China National Association of International Studies, a government think-tank, said China's decision to votewas mainly because the adopted resolution contains voluntary provisions.
"This resolution is a watered down version compared to original requests raised by the US and some of its allies," he told Al Jazeera.
"Furthermore, the key provisions in this resolution are voluntary ... it basically creates a legal justification for countries who want to take those actions as specified in the resolution."