Pentagon officials told top lawmakers in a closed-door briefing on Tuesday that the cost of the war against Iran has already exceeded $11.3bn in its first six days, but the true cost of the opening days of the conflict is likely far greater, according to two people familiar with the matter.

This figure, first reported by the New York Times and confirmed by the Associated Press, in addition to the Guardian, represents the most detailed cost assessment that Congress has received so far as lawmakers seek clarity about the scope and duration of the conflict.

But the estimate, presented during a classified briefing on Capitol Hill, appeared largely limited to munitions expenditures and does not capture the full cost of the opening days of the conflict, one person familiar with the matter told the Guardian. Additional costs to consider include the deployment of forces to the region, medical expenses and the replacement of military aircraft lost in war.

The Guardian reported last week that the US spent about $2bn each day in munitions at the beginning of the conflict before spending fell to $1bn each day. The cost per day is expected to fall further as the war continues, unless the situation escalates.

The people spoke on the condition of anonymity to discuss sensitive operational details. The Pentagon previously declined to comment on inquiries about the cost of the campaign.

The estimate nevertheless provides the clearest picture to date of the scale of the campaign and US forces amassed in the Middle East as Donald Trump’s decision to abruptly start a military conflict against Iran faces mounting scrutiny on Capitol Hill.

The initial strikes relied on sophisticated and expensive precision-guided weapons, including the AGM-154 Joint Standoff Weapon, a glide bomb that can cost between $578,000 and $836,000 per unit. The US navy purchased roughly 3,000 of the munitions nearly two decades ago.

As the campaign has progressed, the Pentagon has switched to less expensive munitions, including the Joint Direct Attack Munition, or JDAM. The smallest JDAM warhead costs about $1,000, while the guidance kit that converts conventional bombs into precision weapons costs roughly $38,000.

The rapid burn rate of the US’s most sophisticated weapons is expected to require Congress to eventually pass a supplementary defense spending package to buy new munitions to backfill stockpiles, a person familiar with the matter said.

But the Trump administration has so far been noncommittal about the duration of the Iran war and its ultimate objectives, leaving lawmakers from both parties increasingly skeptical about approving additional funding for a package they fear could be open-ended.