According to this report , Trump seems to be the one pushing for a larger military attack on the Syria government against the advice of the Pentagon and Mattis:
Talking to Pentagon officials after the apparent gas attack, Mr. Trump called for a more sweeping retaliatory response than the military advised, one White House official said. He asked to consider options that would punish not only the Syrian regime but also two of its sponsors—Russia and Iran [bold mine-DL]. “He’s pressed back” on suggestions from Defense Secretary Jim Mattis that the response should be more limited in scope, the official said.
Whenever Trump makes alarming threats against other states, many people tend to discount them because he is such a changeable windbag so much of the time. In this case, I think we should take Trump’s threats, including his stupid taunting  of a nuclear-armed major power, as an indication of what he genuinely wants to do. Mattis may be able to talk him down to ordering a relatively smaller attack, but judging from this report and Trump’s other statements it seems that the president is almost looking for ways to escalate.
Trump seems to be unusually susceptible to demands that he “do something” in response to an atrocity in a foreign conflict. He presumably remembers how pundits swooned about his “leadership” when he ordered the attack on the Syrian government last year, and he craves that applause and affirmation. He reacts to whatever he sees on television, and he seems to easily influenced by the outlets that flatter and praise him, so if those outlets are telling him to attack that is almost certainly what he will do. Finally, Trump has no problem with ordering dangerous and unnecessary uses of force so long as he thinks they may him look “tough” in the eyes of the world.