Washington (CNN) Top military officials, including Defense Secretary James Mattis, warned President Donald Trump during an afternoon meeting Thursday that he risks escalating US involvement in Syria if he goes forward with the type of aggressive bombing campaign he has pressed for over the past week, according to US and western officials briefed on the conversation.

Trump has pushed military leaders to develop plans for a sustained assault on Syrian regime targets in response to last weekend's chemical attack, the officials said. But Mattis and other members of the President's national security team cautioned Trump during the meeting that such a strategy could pull the US into direct conflict with Russia and Iran.

The resistance has upset Trump, who wanted to take quick action and feels like the options being presented to him don't go far enough, according to the officials.

Nevertheless, there is a view among Trump's national security team that the President's tweets earlier this week -- including one threatening US missiles "will be coming, nice and new and 'smart' " -- forced their hand and made some type of strikes inevitable. But there is an effort to calibrate the response, even as Trump is pressing his team to act.

"Once the President tweeted what he tweeted we have to go forward," one senior administration official said.

Messages are being passed to Moscow about the US and its allies' intentions to create a "lasting deterrent" against the use of chemical weapons again, according to one senior administration official. That includes conversations between Gen. Joseph Dunford, the chairman of the Joint Chiefs of Staff, and his Russian counterpart.

"This is being done with great carefulness and a look as to how we engage," the official told CNN. "Nobody wants to start a war with Russia and Syria. At the same time the Syrians did what they did. So we have to answer the second without starting the first."

Trump huddled with his national security team for roughly 90 minutes Thursday, but the White House said soon after the meeting ended that no final decisions had been made. National security officials were expected to confer again on Friday at the White House, though press secretary Sarah Sanders indicated the session would be among deputy-level officials, not top-ranking aides. A delay in strikes after Trump publicly previewed them earlier this week could allow Syrian, Russian and Iranian forces to better prepare for them, multiple US officials said.

"We're continuing to have ongoing meetings and conversations here at the White House," Sanders said. "When we have any further developments within we'll developments, we'll let you know."

Speaking at a session of the United Nations Security Council on Friday, US envoy to the UN Nikki Haley described a deliberative process.

"This has been a very thorough approach," Haley said. "You don't rush decisions like this. If you rush decisions like this, you make a mistake."

Questions remain about a lack of firm evidence pinning the chemical attack on the Syrian regime, despite expressions of confidence from France and the UK. Mattis raised those concerns during Thursday's meeting at the White House, according to officials. Russia, meanwhile, claimed Friday to be in possession of "irrefutable evidence" the alleged chemical attack was a "staged incident," according to Foreign Minister Sergei Lavrov.

Haley told reporters those claims were absurd.

"We know who did this. Our allies know who did this. Russia can complain all it wants about fake news, but no one is buying its lies and cover ups," she said.

Speaking to reporters at the White House, Sanders indicated the US has "very high confidence that Syria was responsible and Russia also."

Both Prime Minister Theresa May and French President Emmanuel Macron said on Thursday that the Syrian regime was likely responsible for the attack. Trump spoke with both leaders on Thursday evening. In his conversation with May, the two "agreed it was vital that the use of chemical weapons did not go unchallenged, and on the need to deter the further use of chemical weapons by the Assad regime," according to May's office.

Despite foreign allies' expressions of confidence in the Syrian regime's culpability in the attack, US officials have not ventured that far in public. During Thursday's meeting at the White House, Mattis advised Trump to wait for more definitive proof before ordering strikes.

International observers with the Organization for the Prohibition of Chemical Weapons have yet to reach the Damascus suburb of Douma, where the attack took place. The organization said they were due to arrive on Saturday.

Biological samples from the area of the alleged chemical attack have tested positive for chlorine and a sarin-like nerve agent, according to a US official familiar with the US analysis of the test results. A Western official told CNN that the results are not conclusive, but officials suspect the substance used in the attack was a mixture of chlorine, sarin and possibly other chemicals.

Medical sources and activists in Syria say following the alleged chemical attack last Saturday that blood, urine and hair follicle samples were smuggled in batches to Turkey during evacuations by the Syrian regime of rebel groups and their families. But the sources did not know what happened to the samples after they reached Turkey, and it's not clear if those were the biological samples analyzed by the US.

Appearing on Capitol Hill earlier Thursday, Mattis publicly raised his concerns about escalation in Syria. Russian and Iranian forces have bolstered Syrian dictator Bashar al-Assad as he clings to power after a bloody seven-year conflict.

The US and Russia maintain a "deconfliction line" between the US al-Udeid air base in Qatar and Russia's Hmeymim military base in Syria to prevent conflicts. But an accidental US strike on Russian or Iranian positions could dramatically escalate tensions in the region.

"We are trying to stop the murder of innocent people. But on a strategic level, it's how do we keep this from escalating out of control, if you get my drift on that," Mattis said in morning testimony before the House Armed Services Committee.

Speaking before a meeting with farm state lawmakers on Thursday morning, Trump said he and his team were closely monitoring events on the ground.

"We're looking very, very seriously, very closely, at that whole situation," the President said from the Cabinet Room. "We have to make some further decisions. So they'll be made fairly soon."

Trump's new national security adviser John Bolton has been ever-present in the deliberations, US officials said. He sat in the Oval Office with Trump last evening along with chief of staff John Kelly when Trump phoned May, and was the leading voice telling Trump to cancel a planned trip to South America to remain in the United States and monitor the Syria response.

In meetings this week, Bolton has relayed Trump's views that a more muscular response is needed. But he has viewed his role as ensuring Trump has all the necessary information to make an informed decision, according to an administration official.