(CNN) US President Donald Trump has vowed to wipe Islamist terrorism "from the face of the Earth" and says he wants the US to "start winning wars again" -- but he's gotten off to a rocky start in the Middle East.

The US and Iraq are investigating whether a US-led coalition airstrike in the city of Mosul was behind the deaths of more than 100 people on March 17. If it is, it could be one of the greatest losses of civilian life caused by the coalition since it began strikes on ISIS in 2014.

But Mosul isn't Trump's only worry in the region. More than 80 civilian deaths in Syria allegedly caused by the US-led coalition are also being probed. And a raid in Yemen that Trump approved was widely criticized for leaving at least 23 civilians and a US Navy SEAL dead.

All this in the nine weeks Trump has been in office.

The US is intensifying its operations in these conflicts, and in Iraq and Syria, it has boosted its presence on the ground.

The Trump administration has already loosened the rules for counter-terrorism missions in parts of Yemen, allowing the Pentagon to carry more of them out without authorization from the White House. And they are discussing doing the same in Libya and Somalia.

There have been concerns that this relaxing of policy might remove a layer of checks and balances and in turn fuel a rise in civilian deaths.

Here's what's happened so far:

Iraq

In the past three days, 112 bodies have been pulled from the rubble of flattened homes in western Mosul, where Iraqi forces and a US-led coalition are in an intense stage of their fight to flush ISIS militants from the city. The dead are believed to be mostly civilians.

But confusion has swirled over what caused the homes to crumble.

At first, a civil defense group and local officials blamed the carnage on a March 17 coalition airstrike.

A man breaks down in tears after a dozens were killed in Mosul on March 17.

But several theories have since been floated.

The Iraqi military on first inspection of the site thought that ISIS had detonated a large vehicle bomb. Then the head of the Iraqi Counter-terrorism Unit in Mosul claimed that the US-led airstrike had hit the vehicle bomb, causing it to explode

Which version of events is true, if any, is still unknown, but the US and Iraq have both launched investigations into the incident.

The coalition has not denied or confirmed the Iraqi military's account, saying that deaths were still being investigated.

"I tell you, the death of innocent civilians in war is a terrible tragedy, no matter how many, and it weighs heavily on our hearts," Joe Scrocca, a coalition spokesman said on CNN's Amanpour on Monday.

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The fight against ISIS is now at a critical stage, and even with great care, the number of civilian casualties is expected to rise, according to the Soufan Group, a risk consultancy firm.

"As the battlefield shrinks and the fighting intensifies, efforts to achieve the crucial objective of destroying the Islamic State in its current form ... and the moral imperative of protecting civilian life and property, will inevitably become increasingly imbalanced towards the former," it said in a note Monday.

Coalition forces are simultaneously targeting Mosul and ISIS' heartland of Raqqa in Syria, and the Trump administration is intensifying America's presence in both countries.

The number of coalition advisers supporting the Mosul offensive, for example, has risen in recent months. Last month, coalition spokesman Col. John Dorrian said around 450 US advisers were in Iraq . A US defense official told CNN recently that the number had since risen by further deployments in the "low hundreds."

Syria

The US military is also investigating reports of dozens of civilian deaths in Syria allegedly caused by coalition airstrikes.

Local reports said that more than 40 people were killed and dozens were injured in a March 16 airstrike in northern Syria that hit a mosque.

For days, the Pentagon said there were no civilian casualties in the incident, even as numerous social media reports showed images of bodies being carried out of the rubble.

The US military denies it targeted a place of worship, claiming that the strike along the border of Idlib and Aleppo provinces was aimed at a building a mere 40-50 feet (12-15 meters) away believed to be hosting an al Qaeda meeting.

"That case is currently under an assessment right now," Scrocca told CNN. "We have not been able to determine yet the validity of the allegation."

In another sign of the America's greater presence in the conflict, the US-led coalition last week carried out an unprecedented air assault in Syria to retake a vital dam near Raqqa from ISIS.

The assault, which backed rebel fighters in Syria in a major ground offensive, involved flying about 500 local US allies and coalition military advisers to an area where they could attack the dam and neighboring town and airfield.

The attack was also backed by US Marines firing M777 howitzers along with airstrikes carried out by Apache helicopters.

Gen. Joseph Votel, the top US commander in the Middle East, told the New York Times last month that even more American troops may be needed in Syria.

"It could be that we take on a larger burden ourselves," he said. "That's an option."

Yemen

A US military raid in Yemen may have been the start of Trump's Middle East woes

The President approved the operation that left at least 23 civilians, including women and children, dead. A US Navy SEAL also died in the operation. A $75 million helicopter was badly damaged during a hard landing and had to be destroyed.

The White House has maintained that the raid was successful and helped gather important intelligence on the Al Qaeda in the Arab Peninsula militant group.

But some analysts and Trump opponents said the raid was botched, and was a sign of the new government's reckless attitude to civilians.

Senator John McCain, who chairs the Senate Committee on Armed Services, said: "I would not describe any operation that results in the loss of American life as a success."

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The Yemen raid and the decision to relax authorization requirements to carry out counter-terrorism missions there has raised concerns that the Trump administration might do the same in other countries.

A senior US military official told CNN that although the rules on how strikes are authorized were being reviewed, there was no greater tolerance or acceptance of civilian casualties, even if the target is rapidly decided upon and hit.

Afzal Ashraf, a visiting fellow at Nottingham University's Center of Conflict Security and Terrorism, said that this changes could be positive in some circumstances and negative in others.

"It's good that it allows for rapid decision making, so if the military and the CIA find a target, often these targets only show up for minutes. There is not the time to go to the President and ask permission to strike," he said.

"On the other hand, it prevents the scrutiny on decision making, and in most cases, it's good to have a detached view from outside the military to challenge the veracity of the intelligence. If you don't have that challenge, group think and other factors come into account."

What's next?

But there are other reasons the number of civilian casualties could increase.

In western Mosul, a historical enclave of small alleyways and old buildings, the fight is one of dense urban warfare. Avoiding civilians is all the more challenging here.

That is largely to do with some of the weapons the coalition is using, Many are designed for more conventional warfare in larger and less populated battlefields, not densely populated cities, Ashraf said.

"We shouldn't be using weapon in cities, like bombs or artillery weapons, because the chances of collateral damage are huge, especially in cases where Daesh are using civilians as human shields," he said, referring to ISIS by its Arabic acronym.

Scrocca from the coalition explained that officers take care to use munitions that are proportional to their targets.

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"If we're trying to take out some ISIS snipers perhaps on a roof, we're not going to use a large bomb that's going to destroy a building. We're going to make sure that we use a proportionate munition that will kill the fighters but leave the buildings standing," he said.

"We want to return Mosul to the people of Mosul, you know, in one piece," he said.