A US military spokesman said Thursday that Islamic State extremists lost as much as half of their defending force after strikes in recent days in the city

US airstrikes in recent days have killed an estimated 350 Islamic State fighters holed up in the western Iraqi city of Ramadi, an American military spokesman said, suggesting the extremists lost as much as half of their defending force.

Col Steve Warren, spokesman for the US military command in Baghdad, told reporters at the Pentagon that there had been an estimated 600 to 1,000 Isis fighters inside Ramadi, which the extremist group captured in May. Despite this depletion of Isis forces, US officials are reluctant to predict how long it will take to reclaim the city, which is the capital of Anbar province and a key to the Iraqi government’s hopes of restoring its borders.

Defense secretary Ash Carter, speaking separately Thursday, said Iraqi progress in retaking Ramadi has been “disappointingly slow”.

“I am certain it will fall, and we will assist in the making of it fall,” Carter said of Ramadi. He added that the US would be willing to commit US army Apache attack helicopters to the battle for Ramadi, if the Iraqi government requests it and if it would “make a strategically decisive difference”.

Asked about that comment later, Warren said, “Apache helicopters are ready,” if Washington and Baghdad give the go-ahead.

US officials have frequently expressed frustration with how long it has taken the Iraqi army and other security forces to press an offensive in Ramadi, but in recent days, they have pointed to important battlefield progress. On Tuesday, Iraqi forces seized an Isis operations center and the strategic Tamim neighborhood on the outskirts of the city.

With approximately 10,000 troops, including federal police, committed to the fight for Ramadi, the Iraqis vastly outnumber the defenders. Iraqi Maj Gen Ismail al-Mahlawi, head of military operations in Anbar province, said Thursday there are approximately 300 Isis fighters trapped in the center of Ramadi, which lies on the Euphrates river.

Separately, Warren announced that US airstrikes in late November killed three senior Isis leaders, including Abu Salah, described as the group’s financial minister and a holdover from the al-Qaida network.

“Killing him and his predecessors exhausts the knowledge and talent needed to coordinate funding within the organization,” Warren said.

The spokesman said US airstrikes also killed Abu Maryam, an Isis “enforcer and senior leader of their extortion network”, and Abu Rahman al-Tunisi, described as an Isis executive officer who coordinated the transfer of information, people and weapons.

Warren said the three were killed in airstrikes near the northern Iraqi town of Tal Afar.