ROME — When President Trump landed in Saudi Arabia last Saturday on his first foreign trip, he brought with him a $110 billion arms deal. When he arrives at the NATO summit in Belgium on Thursday, he will bring mostly questions, many of them about the war in Afghanistan.

The Pentagon is pushing to reinforce the Afghan army with up to 5,000 more American troops. Some administration officials expected Mr. Trump to make a decision on a deployment before the NATO meeting, which would have laid down a marker for the other alliance members.

But now the president’s decision has been delayed, officials said, after an intense debate erupted in the West Wing over the wisdom of pouring more soldiers into a 16-year-old conflict.

Mr. Trump, they said, wants to gauge what other NATO members are willing to contribute to the military effort before he makes any commitment. The United States is already spending $3.1 billion a month in Afghanistan — a number that aides say weighs on a president who has spoken about the need for greater burden-sharing from NATO allies.