WASHINGTON — Defense Secretary Jim Mattis sought on Thursday to slow down an imminent strike on Syria, reflecting mounting concerns at the Pentagon that a concerted bombing campaign could escalate into a wider conflict between Russia, Iran and the West.

During a closed-door White House meeting, officials said, Mr. Mattis pushed for more evidence of President Bashar al-Assad’s role in a suspected chemical attack last weekend that would assure the world that military action was necessary.

Despite the caution, two Defense Department officials predicted it would be difficult to pull back from punishing airstrikes, given President Trump’s threat on Twitter a day earlier of American missiles that “will be coming, nice and new and ‘smart.’”

Mr. Mattis publicly raised the warning on Thursday morning, telling the House Armed Services Committee that retaliation must be balanced against the threat of a wider war.