"Undoubtedly, such moves will never hide that great crime," President Hassan Rouhani said, according to Iran's state-run Press TV.
Saturday's execution of cleric Nimr al-Nimr and 46 others in a single day on terrorism charges has stirred a vigorous reaction in the Middle East and beyond. Many countries have taken sides, along sectarian lines -- with predominantly Shiite nations like Iran condemning it, while those with mostly Sunni Muslims standing behind Saudi Arabia.
On Tuesday, for instance, Kuwait, whose ruling family and most of its citizens are Sunni, recalled its ambassador to Tehran, citing "torching and sabotage activities" of Iranian demonstrators.
"Such action constitutes a flagrant breach of international conventions and violation of Iran's international commitment over security and safety of diplomatic missions on its lands," the Kuwaiti Foreign Ministry said.
In his remarks in Tehran with Danish Foreign Minister Kristian Jensen, Rouhani defended those who have reacted angrily to the mass execution. This includes this weekend's storming and torching of the Saudi Embassy in Tehran, which spurred Riyadh to cut diplomatic ties.
"It is only natural that a crime against Islamic and human rights will be met with reaction from public opinion," Rouhani said.
Rouhani: Europe has a human rights obligation to act
The United Nations Security Council has condemned "in the strongest terms" the attacks against the Saudi Embassy in Tehran and another Saudi diplomatic mission in Iran after the execution of the cleric infuriated protesters there.
It also called on Iran "to protect diplomatic and consular premises against any intrusion or damage."
Iranian Foreign Ministry spokesman Jaberi Ansari has said his country is committed to protecting diplomatic missions and reiterated that no Saudi diplomats were harmed -- or even present -- during this weekend's attack.
The U.N. Security Council did not address the execution of Nimr, who was convicted of inciting sectarian strife, sedition and other charges after his 2012 arrest.
But others have focused on the cleric, calling Saudi Arabia's decision unjust and taking action in response.
In addition to Saudi Arabia and Kuwait, Bahrain, where a Sunni monarch rules over a predominantly Shiite nation, also severed diplomatic ties with Iran. The United Arab Emirates recalled its ambassador, while Sudan expelled the Iranian ambassador and the entire Iranian diplomatic mission in the country.
The President of Iran, a country that has been criticized over its over human rights record, called on other countries outside the region to also take a stand.
"Criticism should not be responded to with beheading," President Rouhani said. "... We hope that European countries, which always react to issues of human rights, would act on their human rights-related obligations in this case, too."
World powers weigh in
Calling the breakdown in relations between Iran and Saudi Arabia "deeply concerning," U.N. Secretary-General Ban Ki-moon talked to foreign ministers for both nations Sunday to push for peace.
Other countries have done the same, with Turkey urging both sides to "abandon ... the language of threats and a return to the language of diplomacy."
That's the stance being taken by the United States, with Secretary of State John Kerry reaching out to the Saudi and Iranian foreign ministers to try to calm tensions.
State Department spokesman John Kirby said Tuesday morning that his government had "expressed our concerns privately and publicly to the Saudi leaders" about the legal process and executions for several months. But now that they've happened, Kirby said key regional players should use dialogue to work out their differences and not lose focus on other looming issues -- namely the fight against ISIS and ending Syria's years-long civil war.
"We don't want this to impact operations against ISIL, and so far it is not," Kirby told CNN's "New Day," using another acronym for ISIS. "We don't want this to affect the political transition in Syria and the move to get the opposition groups at the table with (President Bashar al-)Assad's regime. ... So far, that hasn't changed either.
"But we're mindful of the potential effects here, and that is why we're working ... so hard."
Kirby insisted that Washington continues to lead in the effort to defeat ISIS and to end Syria's crisis. But he said that it's up to leaders in Tehran and Riyadh to stem the tensions, without the United States forcing the issue.
"This isn't a time for threats and clout and trying to use leverage," the State Department spokesman said. "This is a time for these (countries' leaders) to get together and work this out."
Where do we go from here?
Iran has been a longtime supporter of Assad, while Saudi Arabia has provided the rebel factions fighting Assad with financial assistance and weapons.
It's nothing new that the two countries aren't seeing eye-to-eye.
The schism dates back 14 centuries and has to do with disputes over who should succeed the Prophet Mohammed as leader of the Islamic faith.
Sunni Islam has gone on to dominate the faith -- nearly 90% of the world's Muslims are Sunnis.
The Saudis champion the Sunni branch of the faith, while Iran backs the Shia side.
The execution of the cleric only exacerbated their differences and will play out in the coming weeks.