JERUSALEM — At least three people were wounded yesterday as Palestinian Arab security forces who were trained in an American-funded program battled gunmen in a northern West Bank town long known for its lawlessness.

The operation marked the first major test for a group of Presidential Guard officers who are at the forefront of a $28 million American effort to bolster the Palestinian Authority’s security capabilities through training and equipment. The effort is considered vital as the Palestinian Authority negotiates a peace deal with Israel, which has sharply criticized the authority for not doing enough to crack down on armed groups.

In yesterday’s clashes, one person was critically wounded, security and medical officials said. Two people were later shot in the legs.

Islamic Jihad said two of its fighters were among the injured.

The operation began before dawn with hundreds of Palestinian Arab security officers rolling into the town of Qabatiyeh, a stronghold of armed groups such as Islamic Jihad that have pledged to eradicate Israel. Exchanges of gunfire could be heard throughout the morning as the police forces attempted to impose control.

“If you’re going to Qabatiyeh, you’re not going after car thieves. It’s a tough place,” a senior Western security official who spoke on the condition of anonymity said. “This is a clear indication of resolve by Prime Minister Fayyad and President Abbas.”

Messrs. Fayyad and Abbas lead the Palestinian Authority, which is considered relatively moderate and holds sway in the West Bank.