White House press secretary Karoline Leavitt said the talks were intended to build on what she called an "opening" created by the ceasefire and could become the start of a long-lasting peace in the region.
But she cautioned that "ceasefires are fragile by nature" and said a long-term truce would take time.
The engagement comes as uncertainty persists over shipping through the Strait of Hormuz and over the peace proposals to be discussed in Pakistan.
Leavitt dismissed media reports from Iran that it had again shut the strait in response to intensified Israeli bombing in Lebanon, calling such a move "completely unacceptable".
Trump "wants to see the strait reopened immediately without limitation and that’s something we’re going to hold them to", she said.
She said the ceasefire did not cover Israeli strikes in Lebanon, which Iran says violate the truce.
Earlier, Iranian forces had warned ships in the area they would be "destroyed" if they tried to pass without permission. Leavitt said Iran’s public posture was "different privately" and told reporters Tehran had agreed to open the strait.
Leavitt said the main military aims of “Operation Epic Fury”, including the destruction of Iran’s navy, drone and ballistic missile programs, had been met. She declared an American "victory" and said the nearly six-week operation had "achieved and exceeded its core military objectives."
On the proposed diplomacy, Leavitt said reports of a 10-point Iranian plan were inaccurate and that an initial Iranian offer had been "fundamentally unserious". She said Tehran later submitted a modified proposal after Trump warned that a "whole civilization will die" if no deal was reached.
Leavitt defended Trump’s rhetoric after criticism from across the U.S. political spectrum and concerns about the humanitarian consequences of expanded strikes on Iranian infrastructure.
"He retains the 'moral high ground' over Iran's 'rogue regime'," she said, adding: "His very tough rhetoric and his tough negotiating style is what has led to the result you are all witnessing today".
Asked about reports that China had helped secure the ceasefire breakthrough, Leavitt said there had recently been talks "at the highest level" between Washington and Beijing.
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Source: PAP, BBC, Politico