A US general said Tuesday that he did not know if the United States had a particular "grand strategy" in war-torn Libya, where pro-government forces are battling Islamic State jihadists.

Currently, the United States has only a limited footprint in Libya, even though an estimated 5,000 to 8,000 IS fighters operate there.

Small teams of US special operations forces are working to gain intelligence and US aircraft have conducted at least two strikes, but the Obama administration has preferred to let forces loyal to the Tripoli-based Government of National Accord (GNA) lead the fight against the IS group.

Lieutenant General Thomas Waldhauser, who has been nominated to lead the US military's Africa Command, said he did not necessarily see the level of US engagement changing.

"I am not aware of any overall grand strategy at this point," Waldhauser told lawmakers at a confirmation hearing before the Senate Armed Services Committee.

He also said the current, unspecified number of US troops in the North African country was sufficient for now.

GNA forces are leading a fierce fight to oust the IS group from its stronghold in the coastal city of Sirte, which the jihadists have controlled since June last year.

Despite the deaths of at least 34 pro-government troops in clashes with the IS group Tuesday, Pentagon spokesman Peter Cook told reporters the anti-IS fight had "made progress."

"We're watching the situation in Libya very closely. We understand the potential threat that ISIL poses in Libya and elsewhere," Cook said, using an acronym for the IS group.

Libya spiraled into chaos after longtime dictator Moamer Kadhafi was ousted and killed in October 2011, with two governments vying for power and armed groups battling to control vast energy resources.