BEIRUT, Lebanon — A deadly confrontation worsened on Monday between Lebanon’s armed forces and Islamist insurgents from Syria who seized the border town of Arsal over the weekend in what appeared to be the most serious spillover of the Syrian civil war into Lebanese territory since the conflict began more than three years ago.

The Lebanese Army said in a statement that its forces were engaged in fierce battles with the Islamists in Arsal, where witnesses reached by telephone, including the deputy mayor, said shelling had hit the town from multiple directions and thousands of residents had fled.

Arsal is also one of the temporary homes for many of the Syrian war refugees who have sought sanctuary in eastern Lebanon, and witnesses said Lebanese Army checkpoints were refusing to let the refugees relocate deeper into the country. Some refugees said they were panicking because they had nowhere to go.