Smoke rises from an explosives-laden military vehicle driven by an “Islamic State” suicide bomber.

BAGHDAD — Iraq has not requested air support from the U.S.-led coalition for its campaign to retake Tikrit from “Islamic State” insurgents, a senior military official in the coalition said on Thursday, as the assault on the city remained on pause for nearly a week.

Some Iraqi officials this week said more air strikes are needed to dislodge the militants, who are holed up in a complex of palaces built when Saddam Hussein was in power and have turned the city into a labyrinth of homemade bombs and booby-traps.

A Pentagon spokesman said Iraqi forces essentially had Tikrit encircled but did not appear to have progressed as far in their operation to retake the city as initially suggested in early reporting.

The coalition has been conspicuously absent from the campaign, the largest to be undertaken by Iraqi forces and Iranian-backed Shi’a militia groups since IS overran a third of the country last year.

“We have not been asked by the Iraqi government to conduct air strikes in Tikrit,” said the senior military official in the coalition, declining to speculate why. “We don’t conduct any strikes without the request and agreement of the government of Iraq or the Kurdistan Regional Government.”

More than 20,000 troops and militiamen are taking part in the offensive, which began more than two weeks ago, supported by a relatively small contingent of Sunni fighters from Tikrit and surrounding area.

Having made progress towards Tikrit, retaking surrounding towns before entering the city last week, the offensive slowed and there have been no major advances since Friday.

Iraqi officials say they have paused to await reinforcements, limit casualties, and give remaining civilians one last chance to leave.

The senior military official in the coalition said it was “absolutely normal” that Iraqi forces should stop to regroup before a final assault on the Sunni Islamist militants, now cornered in an area bounded by the river Tigris to the east.

U.S. Army Colonel Steve Warren, a Pentagon spokesman, said Iraqis initially had made statements indicating the fight to retake Tikrit was almost complete.

“We see now that essentially is not the case. The Iraqis’ offensive forces … essentially have Tikrit encircled …,” Warren said. “They haven’t really moved into downtown Tikrit.”

“They have a way to go still,” he added. “Urban warfare is difficult. It’s slow. It’s very plodding. … So this fight’s not over yet.”