He said a final agreement would prevent Iran from obtaining a nuclear weapon and would ensure that Iran's enriched uranium would be "satisfactorily handled," according to CBS.
"I will only sign a deal where we get everything we want," Trump was quoted as saying.
Iran, the US and mediator Pakistan all said on Saturday (local time) that progress had been made in talks on ending almost three months of war.
Trump said he would discuss the latest Iran draft agreement with advisers on Saturday and might make a decision on whether to resume the war by Sunday, he told Axios in a separate interview.
"Either we reach a good deal or I'll blow them to a thousand hells," Trump said, according to Axios.
Trump has vacillated between the two poles of diplomacy and military strike since a ceasefire was declared six weeks ago to allow the sides to come to agreement on Iran's nuclear programme and on reopening the Strait of Hormuz, a critical oil and gas supply route now controlled by Tehran.
