Washington (CNN) President Donald Trump grew irritated with his top military brass and national security team on Tuesday when they advised him an immediate withdrawal of US troops from Syria would be unwise and could not provide a timeline for when American forces could exit, people familiar with the matter said.

In a sometimes-tense meeting of his national security team, Trump complained at length about the amount of American money being spent in the region, which he said had produced nothing for the US in return, according to senior administration officials.

And he continued to question why other countries in the region -- particularly the wealthy Gulf nations -- haven't stepped in.

Despite his annoyance and public statement to the contrary, Trump agreed to hold off on immediately pulling troops from the war-plagued nation, even after airing his displeasure with top national security officials.

The White House declined to comment on the tone of the meeting.

But even one of those incoming advisers -- CIA Director Mike Pompeo , who Trump has tapped to serve as secretary of state -- has told him that an immediate withdrawal from Syria would be a mistake.

The incoming national security adviser, former Ambassador John Bolton, didn't participate in Tuesday's session at the White House. Trump has told confidants that he believes Bolton "has his back" on the Syria matter. It's not clear where Bolton stands on the issue, however, though he has favored actions that thwart Iran's influence in the region. Bolton hasn't commented publicly about Syria since accepting the position last month.

Unanimous view

Military officials have presented an almost unanimous view that withdrawing US troops from Syria now would be a mistake -- a stance that clashes with Trump's stated opinion that "it's time" to come home. Top commanders expressed their sentiments in public on Tuesday, despite Trump's remarks.

During the meeting with his national security council at the White House, Trump was told by top advisers such as Gen. Joseph Dunford, the chairman of the Joints Chiefs of Staff, that leaving Syria now would provide an opening for Russia, Turkey and Iran to advance their own interests in the country, which run counter to the United States'. The leaders of those countries are meeting in Ankara this week to discuss their own path forward in Syria.

At one stage, Dunford asked the President to state explicitly what he wanted to see happen in Syria, according to an administration official.

A joint staff spokesman declined to comment on what Dunford said to the President.

The President responded by saying US troops need to finish their mission against ISIS in Syria within six months, a timeline military officials -- including Defense Secretary James Mattis -- warned would be too short, according to the administration official. Trump responded by telling his team to just get it done.

A US defense official briefed on the meeting rejected that any sort of timeline was discussed. Mattis was definitely not asked to draw up withdrawal options, the official said.

The official said that Trump was focused on ISIS' territorial holdings, questioning why the recapture of ISIS' territory was proving elusive given that the military had made such rapid progress against ISIS in the first year of his administration. The official said Mattis explained the challenges involved with Turkey's incursion into Syria drawing away US-backed allies from the ISIS fight and ISIS' beginning to reconstitute itself in remote positions in the middle Euphrates river valley of Syria.

Speaking Wednesday, White House press secretary Sarah Sanders said Trump was intent on handing responsibility for Syria over to local players.

"We want to focus on transitioning to local enforcement and do that over this process to make sure there is no reemergence of ISIS in a way that takes away some of the progress we have made," she said during a briefing at the White House.

"As the President has maintained from the beginning, he's not going to put an arbitrary timeline. He is measuring it in actually winning the battle, not just putting some random number out there," she said later.

'Besides themselves'

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One person familiar with Tuesday's meeting said attendees left "beside themselves" about how a hasty withdrawal and cutting of funds for recovery projects like restoring water and power and rebuilding roads could affect the future of Syria, and make it more likely that ISIS could return to prominence.

"It is a huge gamble that ISIS is not going to come back and that we are going to rely on others to stabilize Syria," the official said. "The President blasted Obama for a timeline in Iraq, but that is in essence what we have been given."

The White House said in a statement on Wednesday it remains committed to battling the Islamic State, a sign that Trump's desire to withdraw troops won't happen in the near-term. But Trump has told his advisers the remaining elements of ISIS that remain in Syria should be defeated quickly so American troops can return home.

He's also continually returned to what he views as insufficient support from US allies in the region. Sanders said Wednesday that Trump was insistent "our allies and partners in the region, who have a lot more at risk, to put more skin in the game."

That's a sentiment Trump has emphasized in private, going after Gulf nations such as Saudi Arabia and the United Arab Emirates for not providing sufficient resources to battle ISIS.

He's boasted to friends that once the US withdraws from the region, the wealthy monarchs of those nations will need to forgo their private jumbo jets and extravagant lifestyles.

"Without us you wouldn't last two weeks. You'd be overrun. And you'd have to fly commercial," Trump told one Gulf monarch, according to a person Trump later told about the call.

In Tuesday's meeting, Trump expressed optimism that the Gulf nations would provide more money for stabilization efforts in Syria -- including up to $4 billion from Saudi Arabia -- though officials who attended the session said they weren't clear what the basis for Trump's confidence was.

Trump met last month with Saudi Crown Prince Mohammed bin Salman, the country's de facto leader. He spoke by phone this week with the Saudi king and the Emir of Qatar, where the Syria issue arose, according to the White House.