What did Trump say about the likelihood of a US-Iran deal and the conditions under which fighting would resume?

Trump stated there is 'a good chance that something could happen' regarding a US-Iran deal, but warned that if negotiations fail to yield an agreement, 'we go back to doing what we were doing' — meaning a resumption of military action. He attributed Iran’s willingness to talk to the pressure exerted by US strikes, saying, 'The only reason they want to meet is because we’ve been hitting them very hard.'

According to the news, are formal US-Iran negotiations currently underway, and what do Iranian officials say about this?

No formal negotiations are currently taking place, according to Iran’s Foreign Ministry spokesman Esmail Baghaei, who said while 'it’s possible that mediators share messages from the US side about current developments,' there are no official talks. The article also notes it is 'unclear if any substantial negotiations between the US and Iran were taking place,' despite Trump’s repeated claims that a deal was close.

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