Trump had not yet made a final decision about whether to attack and ongoing conversations were described as fluid, sources have told to the BBC’s US partner CBS News.
Leavitt told reporters on Wednesday there were “many reasons and arguments that one could make for a strike against Iran”.
She referred to US strikes in June, adding: “Iran would be very wise to make a deal with President Trump and with his administration.”
Although no breakthrough seemed to have emerged from Tuesday’s indirect talks in Geneva, both sides indicated that there had been steps in the right direction.
Iran said an understanding had been reached with the US on the main “guiding principles” that will frame efforts to resolve the dispute around Tehran’s nuclear programme. Foreign Minister Abbas Araghchi added that work still needed to be done.
The US said “progress was made” and Badr Albusaidi, the foreign minister of Oman, which is mediating the talks, said the negotiations “concluded with good progress” on common aims and technical issues.
Asked about the Geneva negotiations, the White House press secretary said that Washington and Tehran were still “far apart” on some key issues.
“I think you heard from the administration and the state department yesterday that there was a little bit of progress made, but we’re still very far apart on some issues,” Leavitt said.
“I believe the Iranians are expected to come back to us with some more detail in the next couple of weeks, and so the president will continue to watch how this plays out.”
Leavitt declined to say whether Israel would be involved in the US decision.
Earlier in the week, Iran said it had reached an understanding with the US on the main “guiding principles” to resolve their dispute over Tehran’s nuclear programme.
Iran has said it wants to focus discussions on its nuclear programme and the potential lifting of economic sanctions, while Washington indicated previously it wanted Iran’s missile development to be part of any talks.
The US and its European allies suspect that Iran is moving towards the development of a nuclear weapon, something that Tehran has always denied.