Following Thursday's bombing, the authorities temporarily closed ports and airports on Majorca as part of a security operation to prevent those responsible from escaping, causing travel chaos for tourists.
Eta has been held responsible for more than 820 deaths during its campaign for an independent homeland in Spain's Basque region.
The two Civil Guards who were killed in Palmanova - Carlos Saenz de Tejada Garcia and Diego Salva Lesaun - had been inside a patrol car parked outside the El Foc barracks when a bomb planted underneath exploded it, security officials said.
Video footage of the moment after the blast in Majorca
Several people were injured by the powerful explosion on the busy road, which sent the vehicle flying through the air and set it on fire.
Police later defused a second explosive device placed under another civil guard vehicle at a different base on Majorca, officials said.
There has been no claim of responsibility for the attack yet, but Spain's Prime Minister Jose Luis Rodriguez Zapatero said it bore all the hallmarks of Eta.
A memorial ceremony has been held at Palma's cathedral for the two officers
"I want to condemn this new low blow with much rage and pain, but also with much determination," he said in a televised address.
"The criminal attack comes at a time when the civil guards and national police, with the co-operation of French security forces, are striking against the terrorist group as never before," he added.
Mr Zapatero said Eta members were being "arrested earlier and in greater numbers, and this is the way it will continue to be".
"The government has given orders to the security forces to be on maximum alert, to double their work, to increase even more their efforts and to protect themselves from these vile murderers," he added.
"They have absolutely no chance of hiding. They cannot escape. They cannot avoid justice. They will be arrested. They will be sentenced. They will spend the rest of their lives in prison."
Steve Kingstone, Madrid correspondent
The charred wreckage of a patrol car in Majorca, and the shattered facade of a police barracks on the mainland represent a grim birthday message from Eta, as the Basque militant group marks the 50th anniversary of its founding.
In the wake of the Mallorca killings, a stern-faced Prime Minister Jose Luis Rodriguez Zapatero again spoke of defeating ETA "definitively". But after the bloodiest week in months, Spaniards may wonder whether he was speaking more out of hope than expectation.
On Friday morning, Mr Zapatero and members of the Spanish royal family attended a memorial ceremony at Palma's cathedral for the two civil guards, during which he placed medals of honour on their coffins.
Thursday's attack was the deadliest since two Spanish undercover policemen were shot during an operation in south-western France in December 2007.
The BBC's Steve Kingstone in Madrid says that for many months Spaniards have been told by their government that Eta is historically weak, following the arrest of a string of alleged commanders of its military wing, but the past 48 hours have provided chilling evidence to the contrary.
Exactly 50 years after it was founded by a small group of radical Basque students, Eta appears to be making a statement - that it has the capability to strike anywhere, our correspondent says.
With the country in its peak tourist season, and with thousands taking to the roads this weekend for their holidays, police resources will be stretched - amid genuine fears of more attacks, he adds.
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