Trump's comments also brought criticism from Iranians on social media, who recalled their government's offers of support and the candlelight vigils held in Iran after the attacks of September 11, 2001 in the United States.
President Hassan Rouhani said Iran's message was that "terrorism is a global problem", and he called for "regional and worldwide co-operation and unity".
Islamic State claimed responsibility for suicide bombings and gun attacks in Tehran on Wednesday, that killed 17 people.
Iran's foreign minister has branded condolences sent by the White House over recent Tehran attacks as "repugnant". Iran's Revolutionary Guards accused Saudi Arabia, its regional rival, of supporting the attack. But he added in a White House statement that "states that sponsor terrorism risk falling victim to the evil they promote".
Iranian Foreign Minister Mohammad Javad Zarif also denounced the terror attacks, saying "indiscriminate" terror attacks are threatening the Middle East and the rest of the world.
But the group's ability to coordinate this attack, along with its success in planning and inspiring two attacks in Britain in the past two weeks, shows just how complex the matter is.
Sunni-majority Saudi Arabia and Shiite Iran have had strained relations throughout their history and have been involved in a sectarian feud for more than 1,000 years.
All of the fourteen people injured in the early Thursday acid attack in southern Tehran have been released from the hospital, head of Iran's Emergency Medical Services Pirhossein Koulivand said on Thursday.
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World leaders, including Russian President Vladimir Putin, expressed condolences to Iranian President Hassan Rouhani in connection with the terrorist attacks.
State Department spokeswoman Heather Nauert says the U.S.is sending thoughts and prayers to the Iranian people following attacks that struck Iran's parliament and the mausoleum of its modern founder.
Iran is now backing the regime of Syrian President Bashar al-Assad against Sunni rebels and jihadi groups in the war-torn country.
The Security Council reaffirmed that "terrorism in all its forms and manifestations constitutes one of the most serious threats to global peace and security" and said "any acts of terrorism are criminal and unjustifiable".
A picture taken on June 7, 2017 shows the main hall of Iranian parliament with lawmakers gathered during the attack which targeted the complex on June 7, 2017.
The "spilled blood of the innocent will not remain unavenged", the Revolutionary Guard statement said.
"We condemn terrorist attacks anywhere they occur and we condemn the killing of the innocent anywhere it occurs", Jubeir said.
But Republicans and Democrats alike said they are eager to add an amendment that would slap fresh sanctions on Russian Federation in response to USA intelligence conclusions that the Kremlin conducted or approved cyberattacks on U.S. targets in an effort to sway the presidential election.
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