Trump didn't say what the new measures may involve.
Iran's president and foreign minister also may skip next week's high-level meetings at the United Nations as the USA has yet to issue them visas, IRNA reported.
Yemen's Houthi rebels, who have been locked in a war with a Saudi-UAE-led coalition since 2015, claimed responsibility for the attacks, warning Saudi Arabia that their targets "will keep expanding". The Saudi military planned to speak to journalists Wednesday in Riyadh to discuss their investigation "and present material evidence and Iranian weapons proving the Iranian regime's involvement".
Mr Trump and Mr Johnson will both attend the United Nations General Assembly in NY next week.
He told a news conference: "The attack was launched from the north and unquestionably sponsored by Iran".
They condemned the attacks and discussed the need for a united diplomatic response from global partners.
Iran's previous efforts to supply missiles to the Houthis, and the fact that the country uses TJ100 engines in its drone program "do imply that Iran could be behind the Quds-1", Hinz added. Defense Ministry spokesman Colonel Turki al-Malki said the recovered weapons included Iranian Delta Wing unmanned aerial vehicles (UAV) and "Ya Ali" cruise missiles.
"I think the case is definitely becoming stronger for the argument that it wasn't launched from Yemen", he said. He also showed what he said were surveillance videos from the early morning hours that showed the weapons approaching from the north.
On Wednesday, Iranian President Hassan Rouhani blamed the conflict squarely on the U.S. The cruise missile had a small jet engine attached to it, he said.
Concrete evidence showing Iranian responsibility, if made public, could pressure Riyadh and Washington into a response, though both nations were stressing the need for caution.
White House orders Pentagon to offer options as Aramco attack fallout escalates
The message has been sent on Monday via the Swiss embassy, which looks after American affairs in Iran.
"If the United States backs off from its call, repents, and returns to the nuclear treaty it has breached, then it will be able to join the gathering of the parties to the deal (JCPOA) who hold meetings and talk with Iran, otherwise no negotiations will take place between the officials of the Islamic Republic and the Americans at any level, not in NY and not anywhere else", Ayatollah Khamenei stressed. It added that Iran's response wouldn't be limited to the source of the threat, without elaborating.
IRNA separately reported Wednesday that Iran's first delegation for the annual U.N. General Assembly meeting had not left Iran because the USA has yet to issue them visas.
The violence has damped speculation, for now, that Trump might meet Rouhani at the annual United Nations General Assembly next week.
As the host of the U.N.'s headquarters, the U.S.is mandated to offer world leaders and diplomats visas to attend meetings there.
An escalation in tensions between the USA and Iran could push the oil price up again. "We know that Iran have been funding groups like Hezbollah".
Tehran has said it will not negotiate with the USA until America comes back to the Obama-era nuclear deal, which President Trump pulled out of in 2018.
U.S. President Donald Trump said on Wednesday that he has ordered a substantial increase in sanctions against Iran. He did not elaborate. Both nations are US allies and have been fighting against the Houthis in Yemen since March 2015.
On Wednesday, Rouhani defended Yemen's right to respond to Saudi attacks on the country and said Saturday's attack should be considered a "warning" by Yemen's Houthi rebels.
Oil price jump linked to Saudi Arabian attacks sparks energy stock rally
Brent, the worldwide oil benchmark, saw prices surge over 10% Monday to just shy of $67 a barrel. Pompeo said Tuesday that Trump was "prepared to meet with no preconditions".