The military said one of the dead men was an officer. Two other soldiers were injured in the clash at a checkpoint, in which seven militants were killed.
Local media outlets said the fighting took place in the city of Rafah, on the border with Gaza.
An army statement said weapons were seized from the militants.
There was no immediate claim of responsibility for the attack on the soldiers.
The May 7 attack, which took place east of the Suez Canal, was the deadliest by militants on security forces in Sinai in years. A local ISIS affiliate claimed responsibility.
Egypt retaliated with air strikes that destroyed several militants' hideouts and killed nine extremists, the military said. On Wednesday, there were more air strikes that killed seven more militants and destroyed a vehicle.
Egyptian security forces have for years been battling an insurgency in northern Sinai led by a local ISIS affiliate — ISIS-Welayet Sinai.
President Abdel Fattah El Sisi said last month that more than 3,000 policemen and troops had been killed fighting militants since 2013, and that another 12,000 had been injured.
Attacks in Sinai, the capital Cairo, the Nile Delta and the western desert have surged following the 2013 overthrow of president Mohammed Morsi of the now-banned Muslim Brotherhood, amid mass street protests against his divisive, one-year rule.
A major government offensive launched in 2018 slowed the attacks, although militants have continued to target isolated and small police and army outposts and kidnapped civilians or tribesmen who openly support the government.
The UAE condemned Wednesday's attack as “cowardly”, official news agency Wam reported.
“The UAE strongly condemns this cowardly act and stresses its rejection of all forms of violence that [aim] to destabilise security and run counter to humanitarian values and principles,” said Sheikh Abdullah bin Zayed, Minister of Foreign Affairs and International Co-operation.
Sheikh Abdullah restated the UAE’s support for all the measures taken by Egypt to protect its security and stability.
He also offered his condolences to Egypt and the families of the victims while wishing a speedy recovery for the wounded.