Iran live updates: US blockade of Iran's Strait of Hormuz ports to begin Monday

President Donald Trump told ABC News on Wednesday morning that the U.S. may seek a "joint venture" with Iran to safeguard the Strait of Hormuz, following his Tuesday announcement of a two-week ceasefire.

"We're thinking of doing it as a joint venture. It's a way of securing it -- also securing it from lots of other people," Trump said when asked whether he would allow Tehran to charge tolls for shipping to transit the strategic waterway. "It's a beautiful thing," the president added.

Trump also said he would not allow Iran to retain any uranium enrichment capabilities, despite Tehran's repeated assertions that it will not give up its freedom to do so. "There won't be any enrichment," Trump said.

American forces in the region will also not be leaving, Trump said, suggesting they would remain in place to enforce any future agreement.

Trump said he expected peace talks to start on Friday and to move very quickly. The president also confirmed that China played a key role in dealing with the Iranians.

The announcement of a temporary ceasefire "may create transit opportunities, but it does not yet provide full maritime certainty," in the Strait of Hormuz, Danish shipping company Maersk told ABC News in a statement on Wednesday.

Maersk, one of the largest container shipping groups in the world, said it welcomed the announcement of a ceasefire but that, "information and details available remain very limited and we are working with urgency to obtain further clarity."

"Any decision to transit the Strait of Hormuz will be based on continuous risk assessments, close monitoring of the security situation, and available guidance from relevant authorities and partners," the group said, adding that for now, no changes were being made to its services.

The Israel Defense Forces said on Wednesday that it was continuing "combat and ground operations" against Hezbollah in Lebanon, while at least one Israeli airstrike was reported in the southern city of Tyre.

Israeli Prime Minister Benjamin Netanyahu said overnight that the two-week ceasefire with Iran "does not include Lebanon," though Pakistani Prime Minister Shehbaz Sharif said the country was covered by the ceasefire announced on Tuesday.

The IDF issued multiple evacuation warnings in Lebanon on Wednesday morning, including in the city of Tyre and for all residents of Beirut's southern suburbs.

In a late- night social media post following the announcement of a two-week ceasefire deal, President Donald Trump called it "a big day for World Peace!" and claimed that the U.S. "will be helping with the traffic buildup in the Strait of Hormuz."

"There will be lots of positive action! Big money will be made. Iran can start the reconstruction process. We'll be loading up with supplies of all kinds, and just 'hangin' around' in order to make sure that everything goes well. I feel confident that it will," Trump said in the post.

Earlier Tuesday, Trump said that a two-week ceasefire with Iran was contingent on agreeing to "the COMPLETE, IMMEDIATE, and SAFE OPENING of the Strait of Hormuz."

It's unclear when that will happen, and what role the U.S. might play in reopening the critical waterway.

-ABC News' Meg Mistry