Trump in May withdrew the United States from the Iran nuclear deal, which eased sanctions on Iran in exchange for restraints on its nuclear weapons program.
Wicker, who sits on the Senate Armed Services Committee, opposed the controversial Iranian deal under the Obama administration and supported Trump for withdrawing from it in May.
A senior commander of Iran's elite Revolutionary Guards reacted angrily to Trump's threats by saying Tehran would continue to resist its enemies, Iran's Students news Agency ISNA reported.More news: Hamilton: Ferrari celebration a sign of weakness
Also on Sunday, Secretary of State Mike Pompeo launched a blistering attack on Iran in remarks at the Ronald Reagan Presidential Library in California. "BE CAUTIOUS!" Zarif wrote on Twitter. "It can not continue to show irresponsibility as a revolutionary organization that is intent on exporting terrorism, exporting disruption, across the region", said Mattis, a retired Marine general.
"Such policies will unite Iranians who will overcome plots against their country", Iranian Foreign Ministry spokesman Bahram Qasemi said.
In response, Donald Trump sent an explosive, all-caps tweet telling Mr Rouhani to "never, ever threaten the United States again" and "be cautious!".
Trump's national security adviser John Bolton has in the past advocated bombing and invading Iran to enact regime change.
Pompeo did say the USA was willing to talk with Iran, as Trump has said in the past, but real change can only come with change in the regime's behavior: "We are willing to talk with the regime in Iran, but relief from American pressure will only come when we see tangible, demonstrated and sustained shifts in Tehran's policies", he said.
Blocking world leaders on Twitter won't silence them, but it would certainly hamper necessary discussion around their words and actions, the company said.