A senior US senator, John McCain, has described the ousting of former Egyptian president Mohamed Morsi as a coup, in a move that contradicts the White House.

Officials, including Barack Obama, have avoided using the term to characterise the armed overthrow of Morsi's government on 3 July, largely because US law would then require it to cut aid to Egypt.

Since 1979, successive regimes in Cairo have been beneficiaries of US military aid in kind, which works as a gift voucher to select hardware such as fighter jets and ammunition. The aid deal started after former president Anwar Sadat signed a peace treaty with Israel in 1979, a treaty that remains a cornerstone of US foreign policy in the Middle East.

"We have said we share the democratic aspirations and criticism of the Morsi government that led millions of Egyptians into the streets," McCain said at the end of a brief visit to Cairo in which he and fellow Republican senator Lindsey Graham met senior officials.

"We've also said that the circumstances of [Morsi's] removal was a coup. This was a transition of power not by the ballot box."

The visit by the senators, both members of the Senate foreign relations committee, was aimed at pressing for reconciliation between the interim military-led government and the vanquished Muslim Brotherhood, which remains encamped in two parts of the capital, demanding Morsi's reinstatement.

In Washington, the state department's Jen Psaki said: "Senators McCain and Graham are certainly entitled to their opinions … The US government has stated what our opinion is."

The standoff is into its sixth week and a succession of envoys from the EU, African Union and US have done little to shift the seemingly implacable divide between the two sides, which has twice spilled over into deadly violence and continues to destabilise the country.

McCain and Graham arrived in Cairo one day after the deputy secretary of state, underscoring the concern Washington has over the situation in Cairo. Egypt's military chief, Abdel Fatah al-Sisi, has struck a vehement nationalistic posture since ending Morsi's term one year after he was democratically elected. However, Sisi said this week he continues to hold discussions with foreign officials, including the US defence secretary, Chuck Hagel, with whom he speaks daily.

"What happens in Egypt in the coming weeks is very, very critical and will have a decisive impact on this country and in the Middle East as well," McCain said.

Both senators pressed Sisi to release political prisoners, including Morsi, who has been held at a military base several hours outside of Cairo since 3 July. Morsi is being held with two aides, but is understood to have had no visits from his family. He has access to two daily newspapers and two television stations.

A number of Brotherhood leaders, including Morsi, face criminal charges. The allegations have infuriated Brotherhood backers who say they will remain on the country's deeply polarised streets until Morsi is reinstated.

Egypt's military is understood to be readying for an operation to clear both protest sites as soon as this Sunday, when the three-day Islamic festival of Eid al-Fitr finishes. Sisi and his senior officers have twice this week warned the Brotherhood they must leave the camps.

• This article was amended on 7 August 2013. The original version wrongly stated that Lindsey Graham was a Democrat, and that the trip was bipartisan. In fact he is a Republican senator. It was further amended on 8 August 2013 to correct a description of John McCain as a "US official".