Maric, reported to be a businessman who was upset over an ongoing court case, had left a hand grenade at the entrance to the building and was carrying another with its safety pin removed.
'Death before tyranny'
He had given the government a 1400 GMT deadline to agree an "out-of-court settlement" in a property dispute, local media reported.
In a letter to Tadic, Maric said he had no intention of hurting anyone and that "death is better than the tyranny of the regime".
He said the government had seized $1.2m from him in cash, an emerald, securities, computers and documents.
He was arrested and disarmed by police after five hours of negotiations.
A police official described Maric as a "psychiatric case".
"He sent his message to 11,000 email addresses this morning, threatening to blow up himself unless the government agreed to an out-of-court settlement of his claims," he told the Reuters news agency.
Jasmina Stojanov, the president's press aide, Maric had entered the building via an entrance normally used by journalists and visitors.