The amnesty, granted by Klaus and countersigned by Nečas, outraged many Czechs who believe politicians and their friends are able to evade justice.
Amnesties are among the limited powers of Czech presidents. This one, announced on 1 January, was Klaus's first, and came just before the end of his second and final five-year term in March.
The opposition failed to muster the necessary 101 votes in the lower house of parliament to topple Nečas. The centre-right cabinet has survived five such votes since taking power in 2010.
"This undermined the trust in the law in this country," centre-left Social Democrat Vice-Chairman Lubomir Zaoralek said of the amnesty.
"Ask the people who have been robbed, how they feel about their right for fair trial," he told parliament.
Necas defended himself by saying he signed the president's decision in line with tradition, without questioning it.
The amnesty by Klaus, who led the post-communist economic transformation as prime minister in the 1990s, freed over 6,000 prisoners with short sentences, more than quarter of the prison population.
But the most controversial step was that it halted the prosecutions of people in cases that have dragged on for longer than eight years and who face sentences of up to 10 years.
This includes dozens of cases of financial crime from the turbulent and sometimes lawless post-communist economy of the 1990s.
Klaus has repeatedly denied he had any concrete cases in mind when he granted the pardon.
Foreign Minister Karel Schwarzenberg, one of two run-off candidates to replace Klaus in an election next week, criticised Nečas for not informing the cabinet about the amnesty, and sniped at Klaus.
"Either no one cared about who would profit from the abolition, or someone knew too well. Neither option reflects well on the state of justice and rule of law," he said.
The halted investigations include the disappearance of millions of dollars from an investment fund, suspected asset-stripping in a bank that collapsed and a failed housing scheme in which over a thousand people lost millions of crowns.
They also include the case a judge suspected to be part of a ring that forced healthy companies into bankruptcy to sell their assets cheaply to friends.
Public outrage at corruption has risen in the past two years partly because more cases have been uncovered by more aggressive investigations by police and judges