BEIRUT, Lebanon — The Arab nations of the Persian Gulf have some the world’s highest per capita incomes. Their leaders speak passionately about the plight of Syrians, and their state-funded news media cover the Syrian civil war without cease.

Yet as millions of Syrian refugees languish elsewhere in the Middle East and many have risked their lives to reach Europe or died along the way, Gulf nations have agreed to resettle only a surprisingly small number of refugees.

As the migration crisis overwhelms Europe and after images of a drowned Syrian toddler crystallized Syrian desperation, humanitarian groups are increasingly accusing the Arab world’s richest nations of not doing enough to help out.

Accenting that criticism are the deep but shadowy roles countries like Qatar and Saudi Arabia have played in Syria by bankrolling rebels fighting President Bashar al-Assad.