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.