At least two people were killed and at least 10 injured in the attacks on Saturday.
One person was killed in the explosion and police, who initially reported the second incident as an explosion, later said it was two veiled women who had opened fire on a tour bus.
Egypt's Health Minister, Muhammad Awad Tag Eddin, told reporters two women had opened fire and one of them was killed.
Earlier, security officers at the scene of the firing said one of the attackers shot dead the other, before shooting and wounding herself.
An unidentified person was killed in an explosion under a bridge behind the popular Egyptian Museum in central Cairo that also injured at least four foreigners.
Two Israelis, an Italian, a Russian and four Egyptians were hurt in the blast, which occurred around 4:00 pm (1300 GMT) behind the popular Egyptian Museum in central Cairo on Saturday, police said.
Security sources told Aljazeera's correspondent in Egypt the person killed might be the bomber and reported his name as Ihab Yusri.
The sources said they did not know the exact casualty toll from the bombing near the museum, the main Pharaonic museum in the country and a popular tourist destination.
Also in April, a man killed himself and three tourists when the bomb he was carrying exploded among a group of tourists in a Cairo bazaar.