He added that the Trump administration will work to limit Iranian influence through efforts beyond the nuclear deal, though he did not specify what measures might be taken. Israel says it will not allow Iran to establish a permanent military presence in Syria, fearing the Iranians use it to launch attacks.
The US has more than 2,000 troops in Syria.
Speaking after a North Atlantic Treaty Organisation foreign ministers' meeting in Brussels on Friday, Pompeo said Trump had not taken a decision on whether to abandon the deal but was not likely to stick to it without substantial changes.
"Iran must be stopped", the premier said.
The diplomat also said that Pompeo's claims about Iran's role in Yemen were aimed at deflecting the attention of the global community from Saudi aggression against Yemen.
The deal President Trump has until May 12 to decide if the United States will state a part of.
Israeli Prime Minister Benjamin Netanyahu will make a televised announcement Monday evening in what his office said would disclosing "dramatic news" regarding the nuclear agreement with Iran.
US Secretary of State Mike Pompeo is using the Middle East leg of his first trip overseas as America's top diplomat to call for concerted global action to punish Iran for its missile programs.More news: Manchester City pass 100-goal mark in West Ham win
It was Pompeo's first trip overseas in his new position. Earlier in the day, Pompeo met with Saudi Arabia's King Salman after arriving in Riyadh the previous evening and dining with Crown Prince Mohammed Bin Salman.
"Iran supplies the missiles that the Houthis fire into Saudi Arabia, threatening civilians", he said.
On Qatar, the US officials said they do not blame one side or the other, but want Riyadh and Doha to sort out the stand-off themselves. "When these groups are given safe haven, the US homeland is at risk".
New U.S. Secretary of State Mike Pompeo on Sunday called for unity among the Gulf countries, in an apparent attempt to resolve the ongoing conflict between four Arab states and Qatar.
"(Iran) supports proxy militias and terrorist groups. Qatar denies the charges.
Poor targeting by the Saudis in airstrikes, as well as the kingdom's blockade of Yemeni ports, have done much to worsen the humanitarian situation in Yemen, and Pompeo told Jubeir on Saturday that Yemen must have easy access to humanitarian and commercial goods, along with fuel, the state department official said. "Unlike previous administration, we are not going to neglect vast scope of Iranian terrorism", he underlined.
Pompeo is on a state visit to Saudi Arabia, the first leg of his Middle East tour. They have criticized the US move and all but cut off ties with the White House.
But the snub by Pompeo, who broke decades of tradition by not meeting any Palestinian officials during the current visit, made the US position clear. "And by recognizing Jerusalem as the capital of Israel and the seed of its government, we are recognizing reality". "In fact, Iran has only behaved worse since deal was approved", Pompeo said.