The memorandum of understanding (MoU) brokered by Pakistan and Qatar less than two weeks ago committed the countries to halt military operations on all fronts, including Lebanon, and immediately reopen the Strait of Hormuz, through which about 20% of global oil and gas shipments pass.
They also gave themselves at least 60 days to reach a final deal that covers Iran's nuclear programme, US sanctions and a permanent truce.
Pakistani and Qatari mediators said encouraging progress was made at the first round of talks held in Switzerland a week ago, which US Vice-President JD Vance and Iran's Parliamentary Speaker Mohammed Bagher Ghalibaf attended.
They also said a "communication line" had been formed to enable the safe passage of commercial vessels through the Strait of Hormuz.
But that failed to prevent the recent exchanges of strikes, which began when Iran attacked a cargo ship on Thursday following efforts to open Oman's territorial waters to both inbound and outbound traffic on the southern side of the strait. Iran had warned vessels that the only route was through its own waters on the northern side.
On Sunday night, a US official said both sides would "stand down for now", and that vessels could "move freely" in and around the strait. Technical talks would also "continue on all areas of the MoU", the official added.
The next day, Iran's deputy foreign minister and lead technical negotiator, Kazem Gharibabadi, denied that there were plans for technical talks this week.
US President Donald Trump responded by saying that Iran had requested a meeting in Qatar's capital on Tuesday, and White House Press Secretary Karoline Leavitt announced that Witkoff and Kushner would fly to Doha for "high-level meetings".
On Tuesday, Qatar's foreign ministry spokesman told a news conference that the two US envoys had arrived in Doha for talks with mediators but not Iranian officials.
"The talks will be around all regional issues which are of concern, including, of course, the negotiations with Iran, but also including Lebanon and other files in the region," he said.
"So, they are not here for direct negotiations with the Iranians or related meetings."
He added: "To the best of my knowledge, there are no direct meetings scheduled between the two parties in the coming days."
A senior Trump administration official told the BBC's US partner CBS News that very positive conversations had been held between Witkoff, Kushner and regional leaders.
CBS reported the official as saying good progress in technical talks continues.
Ansari confirmed that technical talks between lower-ranking officials would continue this week and could later be elevated to a senior level.
"We have a track on the nuclear side. We have a track on the economic and state performance issue. We have a track on security and the regional security," he added.
Iranian Foreign Ministry spokesman Esmail Baqai told a news conference in Tehran that Iranian officials were likely to hold talks with mediators in Doha on Wednesday to discuss implementation of provisions in the MoU, including one concerning the release of Iranian assets frozen under US sanctions.
"No meeting at any level with the American side has been scheduled for the coming days," he added.
Ansari said the release of $6bn (£4.5bn) of the $12bn in frozen Iranian assets held in Qatar depended on progress in talks between the US and Iran that had not yet happened.
Baqai also said that Iran would "do whatever is necessary to safeguard its interests" over the Strait of Hormuz and implement related provisions in the MoU.