Trump's national security adviser, Michael Flynn, recently said Iran was being put "on notice" after it conducted a missile test.
Iranian President Hassan Rouhani addressed this in a speech on Friday, stating,
Some inexperienced figures in the region and America are threatening Iran. They should know the language of threats has never worked with Iran. We are not seeking tension but we are united before bullying and any threat.
Images of the rallies were spread across social media, and there was particular alarm over the fact many Iranians were chanting "Death to America."
The phrase became a trending topic on Twitter.
But "Death to America" is a decades-old political slogan that is frequently misinterpreted.
Iranians are definitely angry with Trump right now, but he did not inspire this slogan.
As Foad Izadi, an assistant professor of world studies at the University of Tehran, explained to USA Today,
[The slogan] means death to American foreign policy. [Iranians] have problems with the American government, not the American people. When you walk around town, and people see you're an American, everyone wants to take care of you.
If you take a look at US foreign policy in relation to Iran, it makes sense why many Iranians feel this way.
They are not shouting for the death of Americans, they are shouting for the death of policies that have led to a lot of suffering in Iran.
Yes, it's alarming to hear someone call for "death" to your country, but it's important to understand what this chant really means and what inspired it.
People in Iran shouted "Death to America" during Friday's rallies, but it doesn't mean what you might think.
Iran and the US have had a tense relationship for decades.
In 1953, the CIA (along with the British) orchestrated a coup in Iran, which overthrew the government of the democratically elected Prime Minister Mohammad Mosaddeq and placed the pro-American Shah Mohammed Reza Pahlevi in power.
Mosaddeq nationalized Iran's oil, and the US government and its British pals were not fans of this idea.
In short, this was all about oil and ensuring the West could maintain access to it (not much has changed in terms of US foreign policy and the Middle East).
For decades, the Shah lived lavishly as regular Iranians suffered under a dwindling economy and his repressive policies.
The American orchestrated coup in Iran backfired in a massive way in 1979 with the Islamic Revolution and the subsequent hostage crisis.
The Islamic Revolution was fueled by anti-American and anti-Shah sentiment.
Ultimately, it led to the Shah's downfall and Iran became an Islamic republic.
Amid all this, Iranian students angry with America over its relationship with the Shah — who was in the US receiving cancer treatment — stormed the US embassy and took 60 hostages.
The hostage crisis lasted 444 days, setting the tone for decades of animosity between the US and Iran.
President Obama attempted to improve US-Iran relations, but Trump is poised to backtrack on this in major ways, especially regarding the Iran nuclear deal.
Long story short, this is why people in Iran shout, "Death to America!"
It's a product of a long, complicated and rocky history between the US and Iran.
A lot of Iranians actually really like America, and many were pretty vocal about it on Friday.
Many Iranian's at Friday's rallies carried posters that thanked Americans for protesting Trump's controversial travel ban.
Many Iranians also flooded social media all week requesting people not burn flags with the hashtag #LoveBeyondFlags.
When it comes to foreign policy, and especially US-Iran relations, it's vital to keep things in perspective and recognize history.
But, it's important to remember people and governments are not one in the same.
That is certainly true in the US, where Donald Trump is extremely unpopular and has historically low approval ratings.
In other words, the words and deeds of the Iranian government are not necessarily representative of how all people in Iran feel.
America and Iran have a complicated relationship, be wary of buying into the propaganda emanating from both sides.