Egyptian President Hosni Mubarak has pledged to hunt down those behind the bombs which killed at least 88 people in the resort of Sharm al-Sheikh.
The bombs come at the height of Sharm al-Sheikh's tourist season
Speaking after visiting survivors, he said the attacks only increased Egypt's determination to eradicate terrorism.
In the worst attacks in decades in Egypt, three explosions - including two apparent car bombings - devastated a hotel, a car park, and a market.
Most of the dead are Egyptians, but foreigners are among the victims too.
An Italian man on his honeymoon and a Czech citizen have been confirmed dead and at least 20 of those injured are thought to be foreign.
The blasts came within minutes of each other in the early hours of Saturday, when the bars and markets of the Red Sea resort were busy.
In the most devastating attack, a bomber rammed his car into the Ghazala Gardens hotel in Naama Bay, according to an eyewitness.
The front of the luxury hotel was destroyed in a huge explosion.
A few hundred metres away, a bomb went off in a car park near the Moevenpick Hotel, causing widespread damage and casualties.
In the Old Market area, about 4km (2.5 miles) away, 17 people - believed to be Egyptian - were killed by another suspected car bomb, rescue officials said.
"This will only make us more determined to pursue terrorism and eradicate it," said President Mubarak after visiting the bomb scenes.
"We will not give in to its blackmail, or seek a truce."
Egyptian Interior Minister Habib al-Adli and said police were following leads.
He added that investigations appeared to show a connection with the bombings that killed 34 people last October in the resort of Taba, further north.
Egypt has blamed those attacks on a Palestinian man leading an unaffiliated group.
Security sources say more than 30 people have been arrested in the Sharm al-Sheikh area - but it is unclear whether they are suspected of having close links with the bombers.
In a statement posted on an Islamic website, a group calling itself the Abdullah Azzam Brigades, al-Qaeda, said it carried out the bombings. However, the statement did not appear on major al-Qaeda websites and it was impossible to authenticate the claim.
US Secretary of State Condoleezza Rice, on a visit to neighbouring Israel, denounced "the horrific terrorist bombings".
She said Egypt and the US would "confront and defeat this scourge that knows no boundary and respects no creed".
The bombings happened at the height of the summer tourist season, and coincided with an extended holiday weekend to mark the anniversary of the 1952 Egyptian revolution.
The previous worst attack in Egypt was in 1997, when Islamic militants killed 58 foreign tourists and four Egyptians near the southern city of Luxor.
Tourism is Egypt's most lucrative industry, worth about $6.6bn a year.