A surge in attacks on deployed U.S. forces has roiled some within the Defense Department, where officials, frustrated by what they consider an incoherent strategy for countering the Iranian proxies believed responsible, acknowledge the limited retaliatory airstrikes approved by President Biden have failed to stop the violence.

“There’s no clear definition of what we are trying to deter,” said one defense official, who like others spoke on the condition of anonymity to be candid. “Are we trying to deter future Iranian attacks like this? Well, that’s clearly not working.”

Seething anger in the Middle East over U.S. support for the Israeli military campaign in Gaza, where thousands of Palestinian civilians have been killed in the past six weeks, has heightened concern among Biden and his deputies that any overreaction to the attacks on U.S. personnel could incite a wider conflict. In conjunction with the airstrikes, administration officials have urged Tehran repeatedly over the past month to rein in the militia groups it supports, cautioning that the United States has “the right” to respond “at a time and place of our choosing.” But those warnings have gone unheeded.

Since Oct. 17, U.S. troops in Iraq and Syria have faced near-daily assaults from rocket fire and one-way drones, recording at least 61 incidents and about as many injuries in that span. Pentagon data obtained by The Washington Post shows that the attacks have targeted 10 bases used by American personnel who are spread across both countries.

In response, Biden has authorized three rounds of airstrikes, all in eastern Syria. The most recent, on Nov. 12, targeted sites the Pentagon identified as used by Iran’s Islamic Revolutionary Guard Corps and “Iran-affiliated groups.” A U.S. official said that as many as seven militants were killed, a “rough estimate” as the United States continues to assess the results.

The strikes have destroyed purported warehouses holding weapons and ammunition, a command post and a training facility, officials have said. Yet each operation has failed to slow the drumbeat of hostile activity, which in all cases resumed almost immediately. The 61 attacks on U.S. troops have come at a startling frequency as well: There were about 80 similar incidents between January 2021 and March of this year, the Pentagon has said.

A senior defense official said the Pentagon has provided additional options to the president beyond the actions that have been taken to date. This person affirmed, too, that within the Defense Department there is growing doubt about the present approach.

In a statement, National Security Council spokesperson Adrienne Watson said that Biden has demonstrated that “he will never hesitate to take action to protect U.S. forces” and that the president is “fully prepared to take further measures as needed at any given moment to protect our people.”

Iran has long provided support to militias seeking to dislodge the American presence in Iraq and Syria, where approximately 3,500 troops are deployed to prevent a resurgence of the Islamic State terrorist group. Tehran also backs Hezbollah in Lebanon, whose leaders have threatened to open a new front against Israel, and the Houthi rebels in Yemen. The Pentagon said that Houthis destroyed a $30 million U.S. Reaper drone over the Red Sea in recent days, and U.S. warships have in the past few weeks intercepted weapons fired from Yemen in the direction of Israel.