The presidential office said in a statement that Lula had decided to suspend the top officials until an investigation into the allegations was complete. The alleged spying was described as "abominable".
Opposition leaders had earlier demanded an inquiry into a magazine report about the spying, the latest scandal to hit Lula's government.
Veja, the country's leading news magazine, reported on the weekend that the Brazilian Intelligence Agency, or Abin, spied on Supreme Court President Gilmar Mendes and tapped his telephones. It published what it said was a transcript of a private telephone conversation Mendes had with a member of Congress.
An Abin agent who provided the transcript said such illegal phone tapping of authorities was common and also included the head of the Senate and two cabinet members, Veja reported.
Lula held urgent talks for most of Monday with Mendes, the Senate speaker and several Congress members who expressed their concern and demanded those responsible to be punished.
"Somebody has to be sacked. If the justice minister is at fault, let it be him then," said Demóstenes Torres, of the opposition DEM party
The Brazilian president was surprised and outraged at the possibility of the Supreme Court chief being secretly recorded his spokesman Marcelo Baumbach told reporters earlier. Abin said it was investigating the accusations but had confidence in its staff.
Other government officials joined the opposition in condemning the alleged spying as an attack on democracy and a throwback to the days of Brazil's military dictatorship when intelligence services uncovered dissidents, some of whom were tortured or killed.
Critics say Abin, which reports to Lula's institutional security adviser, lacks transparency and external controls.
Most of the legislators suspected of being spied on are in opposition parties, and Mendes is presiding over a high-profile case involving a prominent banker, politicians and businessmen.
Mercopress