WASHINGTON — Even as the Obama administration defends the NATO-led air war in Libya, the latest violent clashes in Syria and Jordan are raising new alarm among senior officials who view those countries, in the heartland of the Arab world, as far more vital to American interests.

Deepening chaos in Syria, in particular, could dash any remaining hopes for a Middle East peace agreement, several analysts said. It could also alter the American rivalry with Iran for influence in the region and pose challenges to the United States’ greatest ally in the region, Israel.

In interviews, administration officials said the uprising appeared to be widespread, involving different religious groups in southern and coastal regions of Syria, including Sunni Muslims usually loyal to President Bashar al-Assad. The new American ambassador in Damascus, Robert Ford, has been quietly reaching out to Mr. Assad to urge him to stop firing on his people.