Tehran was rocked by fresh explosions and Israel was targeted by missiles on Wednesday, with Iran rejecting the existence of negotiations after Donald Trump suggested an end to the war within "two or three weeks", deal or no deal.

Triggered on February 28 by Israeli-American strikes, the war in the Middle East, which has killed thousands and shaken the world economy, shows no sign of abating.

Several neighborhoods in Tehran were awakened by explosions Wednesday morning, with airstrikes damaging the perimeter wall of the former US embassy. Missiles fired from Iran and Yemen targeted Israel, while in the United Arab Emirates, a Bangladeshi national was killed by debris after a drone attack was intercepted.

The US president is expected to "provide important new information on Iran" in a speech scheduled for later today, at 9:00 PM (1:00 AM GMT Thursday) according to the White House.

Trump, who has been alternating between threats and reassuring statements for weeks, suggested on Tuesday evening that the conflict was nearing its end: "All I have to do is leave Iran and we will do that very soon," he said, mentioning a timeframe of "two, maybe three weeks."

- No longer an "existential threat" -

He, who on Monday had promised to "annihilate" the strategic Iranian island of Kharg as well as oil wells and power plants if an agreement was not reached "quickly" on the reopening of the Strait of Hormuz, this time asserted that the conclusion or not of an agreement was "of no importance".

One fifth of the world's oil usually passes through this strategic sea route, which has been blocked by Iran since the beginning of the conflict.

Iran, for its part, claims not to have responded to the 15-point American plan, submitted last week by Donald Trump to end the war, still refusing to talk about negotiations.

"I am receiving messages directly from (US special envoy Steve) Witkoff, as before, and that does not mean that we are in negotiations," Foreign Minister Abbas Araghchi stressed on Al Jazeera.

Just as Donald Trump was hinting at a way out of the conflict, his Israeli ally deemed that Iran no longer constituted an "existential threat".

"We have broken the power of the Iranian terrorist armies" by preventing Iran from "rushing towards the development of nuclear weapons and tens of thousands of ballistic missiles," Israeli Prime Minister Benjamin Netanyahu asserted. "They can no longer threaten our existence."

For him, "the campaign is not over (...) we will continue to crush the terrorist regime, we will strengthen the security zones around us and we will achieve our objectives."

- Market hopes -

Buoyed by hopes of de-escalation, markets rebounded: in Paris, the CAC 40 was up 1.75% by mid-morning, while in Tokyo, the Nikkei closed 5.24% higher. At the same time, the price of Brent crude oil fell back below $100 a barrel.

Off the coast of Qatar, an oil tanker was damaged by a missile strike attributed to Iran. Kuwait and Bahrain reported fires, at their airport and a company's premises respectively, following attacks blamed on Iran.

In Israel, rescue services reported 14 injured after further Iranian missile strikes.

The country also suffered another attack from the Houthis, a Yemeni armed group allied with Tehran, their third since joining the conflict on Saturday. In their statement, they claimed to have targeted "sensitive sites" in the south of the country.

In Tel Aviv and its region, AFP saw rescue workers taking care of children, as well as damaged cars and broken windows on the second floor of a residential building.

On the other side, Iranian state television announced explosions in the north, east and center of Tehran on Wednesday morning, before Israel said it had carried out a "wave of large-scale strikes" in the capital.

According to the Mehr news agency, residential buildings were hit by strikes, causing several injuries.

The US military also "dropped precision munitions on underground military targets located deep inside Iran," according to the US Central Command for the Middle East (Centcom).

- "New occupation" of Lebanon -

The European Union has called on Iran to guarantee "freedom of navigation" in the Strait of Hormuz, after an Iranian parliamentary committee approved a draft law to impose transit fees on ships passing through the waterway, according to state media. The legislation includes a "no-passage" order for the United States and Israel.

Donald Trump pointed out that "if France or any other country wanted its oil or gas, they would go straight to the Strait of Hormuz (...) and they would manage on their own."

In Lebanon, which has been bombarded by Israel since early March, authorities announced seven new deaths overnight, while the Israeli army boasted of having killed a "senior commander" of Hezbollah and a "high-ranking terrorist" in the Beirut region.

The pro-Iranian Shiite movement dragged Lebanon into the war on March 2 by launching an attack on Israel to avenge the death of Iranian Supreme Leader Ali Khamenei.

Israeli Defense Minister Israel Katz warned that his country intended to occupy part of southern Lebanon once the war was over, with Beirut worried about a "new occupation" of the country, as was the UN.