"Of course, the Saudi government, in order to cover up its crime of beheading a religious leader has resorted to a strange measure and has severed its ties with the Islamic Republic," Rouhani
said during a meeting with Danish Foreign Minister Kristian Jensen in Tehran, adding that "undoubtedly, such moves will never hide that great crime," according to Iran's state-run Press TV.
Rouhani defended those who have reacted angrily to the mass execution. Part of that anger was expressed over the weekend when a group stormed and torched 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.
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 such as Iran condemning it, and predominantly Sunni nations such as Kuwait, supporting Saudi Arabia.
On Tuesday, 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.
Rouhani: Europe has a human rights obligation to act
The United Nations 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 it did condemn "in the strongest terms" the attacks that followed -- on the Saudi Embassy in Tehran and another Saudi diplomatic mission in Iran after the execution of the cleric infuriated protesters there -- and urged 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.
Despite such assurances, many in the region are siding with the Saudis.
In addition to Saudi Arabia and Kuwait, Bahrain -- where a Sunni monarch rules over a predominantly Shiite nation -- also severed diplomatic ties with Iran on the heels of the attacks on Saudi diplomatic missions in Iran.
The United Arab Emirates recalled its ambassador, while Sudan
expelled the Iranian ambassador and the entire Iranian diplomatic mission in the country.
Rouhani, like other Iranian officials, has stood his ground.
"Criticism should not be responded to with beheading," the Iranian President 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."
Kerry 'very concerned,' official says
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.
"The Secretary is very concerned with the direction this thing is going," a senior State Department official said. "It's very unsettling to him that so many nations are choosing not to engage.
"With so much turmoil in the region, the last thing we need is for people not to be having conversations."
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 yearslong 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
"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."
Will this affect Iran nuclear or Syria peace talks?
A second State Department official said it is difficult to figure out what either side, specifically Saudi Arabia and Iran, hope to achieve from this commotion. Do the Saudis and their allies want to hold up negotiations focused on Iran's nuclear program and ending sanctions against Iran? Or is it an effort to affect what happens in Syria, where Iran has been one of Assad's few notable allies
and Saudi Arabia has given financial aid and weapons to rebels fighting him?
Kirby said Washington continues to lead the effort to defeat ISIS and to end Syria's crisis. But he said 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."
The tensions between the Sunni and Shiite arms of Islam date back 14 centuries to the schism over who should succeed the Prophet Mohammed as its leader.
Today, nearly 90% of the world's Muslims are Sunni. Still, there are powerful Shiite players in the world, like Iran. And something like Nimr's execution is sure to only exacerbate differences between the sects.
The U.N. special envoy on Syria insisted Tuesday that he's gotten assurances from the Saudis "that the current regional tensions will not have any negative impact" on efforts to resolve a civil war that's left hundreds of thousands dead and forced millions to flee.
The envoy, Staffan de Mistura, said after meeting Saudi Arabia's foreign minister in Riyadh: "This, for us, is very important because we cannot afford to lose this momentum, despite what is going on in the region."