Egypt says it has bombed Islamic State (IS) targets in Libya, hours after extremists published a video showing the apparent beheadings of Egyptian Christians.
State TV said the dawn strikes had targeted camps, training sites and weapons storage areas.
Earlier, President Abdel Fattah al-Sisi said Egypt had the "right to respond" against IS.
A video has emerged showing a group wearing orange overalls being forced to the ground, with at least 10 people decapitated.
IS militants claim to have carried out several attacks in Libya, which is in effect without a government.
Twenty-one Egyptian workers, all Coptic Christians, were seized in December and January from the coastal town of Sirte in eastern Libya, under the control of Islamist groups.
The video of the beheadings was posted online by Libyan jihadists who pledge loyalty to IS.
The killings were described as "barbaric" by al-Azhar, the highly regarded theological institution which is based in Egypt.
Egypt's military said the air strikes were "to avenge the bloodshed and to seek retribution from the killers".
"Let those far and near know that Egyptians have a shield that protects them," it said.
The statement said all planes involved in the operation had returned safely.
Earlier, President Sisi said: "Egypt reserves the right to respond at the proper time and in the appropriate style in retaliation against those inhuman criminal killers.
"Egypt and the whole world are in a fierce battle with extremist groups carrying extremist ideology and sharing the same goals."
Egypt has declared seven days of national mourning.
Leading international condemnation, the United States called the purported killings "despicable" and "cowardly".
Libya has been in chaos since 2011 and the overthrow of its then-leader Muammar Gaddafi.
Since then, numerous militia groups have battled for control.
The head of the US Defence Intelligence Agency warned last month that IS was assembling "a growing international footprint that includes ungoverned and under-governed areas", including Libya.
On Sunday, Italy closed its embassy in Tripoli. Italy, the former colonial power, lies less than 750km from Libya at the shortest sea crossing point.
Despite the turmoil in Libya, thousands of Egyptians go to the country looking for work.
"These people are not in Libya for tourism, for joy, to steal or even to beat others, these people went to Libya to work and earn some money," said Shehata Walham, the brother of one of those killed.
There had been demonstrations in Egypt calling on the government to do more to secure the release of those held.