President Donald Trump has claimed his administration had "very good discussions" with Iran all day Tuesday, raising hopes for a possible, quick end to the five-month conflict.

Oil prices fell and stocks jumped in Asian trade Wednesday, ‌after Wall Street hit record highs on hopes that a deal could soon be reached to restore traffic through the blockaded Strait of Hormuz.

"They had an all-day negotiation," Trump told Fox News' "@ Night" show. The Strait of Hormuz "is going to be open very soon," Trump added. "If they back out again, they are going to get hit really hard."

Trump has ​often threatened massive strikes if Tehran did not reach an agreement and then cited progress in talks that have so far failed to ​end hostilities.

Axios, citing two regional sources and a U.S. official, reported the U.S. and Iran are closing in on an ⁠interim agreement to reopen the strait with the agreement of Oman, which controls part of the waterway. The report said Washington was aiming for an ​announcement Wednesday.