CAIRO — The Libyan Parliament voted on Sunday to dismiss the prime minister it chose less than four weeks ago, deepening a leadership crisis at a moment when the country’s transitional authorities are under intense pressure to catch the killers of the American ambassador, J. Christopher Stevens, and to stop the prevailing lawlessness that led to his death.

With the dismissal of Prime Minister Mustafa Abu Shagour, Libya now also effectively lacks ministers of defense and interior, the officials most responsible for apprehending the attackers and reining in the local militias that now control the streets. Former interim ministers still hold those titles, but they were written off months ago as hopelessly weak, and their subordinates now describe them as all but absent; Mr. Abu Shagour’s efforts to win approval for a new cabinet failed.

The government has not managed to question or detain even the most obvious suspects in the attacks on the American diplomatic mission in Benghazi where the ambassador died nearly four weeks ago. Leaders of Ansar al-Shariah, the main militia that witnesses saw mounting the attack, are still at large.

And the evident incapacity of the Libyan authorities, in turn, puts pressure on the Obama administration, which must weigh unilateral military action to capture or kill the attackers against the chance that such steps on Libyan soil could produce a backlash from the only Arab populace that now views Washington positively.