WASHINGTON — The Pentagon has presented the White House with the most detailed set of military options yet for attacking the growing Islamic State threat in Libya, including a range of potential airstrikes against training camps, command centers, munitions depots and other militant targets.

Airstrikes against as many as 30 to 40 targets in four areas of the country would aim to deal a crippling blow to the Islamic State’s most dangerous affiliate outside of Iraq and Syria, and open the way for Western-backed Libyan militias to battle Islamic State fighters on the ground. Allied bombers would carry out additional airstrikes to support the militias on the ground. The military option was described by five American officials who have been briefed on the plans and spoke about them on the condition of anonymity because of their confidential nature.

Defense Secretary Ashton B. Carter outlined this option to President Obama’s top national security advisers at a so-called principals meeting on Feb. 22. But the plan is not being actively considered, at least for now, while the Obama administration presses ahead with a diplomatic initiative to form a unity government from rival factions inside Libya, administration officials said.

Even so, the United States military is poised to carry out limited airstrikes if ordered against terrorists in Libya who threatened Americans or American interests, just as it did against an Islamic State training camp in western Libya last month.