One of the letters contained a detonator, police and judicial officials said in Paris on Friday.
The group, which called itself AZF, has issued threats in the past. It sent the two letters on Thursday to Chirac and to the Interior Ministry.
It threatened to take action in May if it did not receive a payoff, officials from the prosecutor's office said, without providing details.
Investigators were analysing the letters, posted in France, and trying to identify the group and stop it from acting, the officials said.
In 2004, the AZF threatened to
bomb railway targets
They declined to disclose the nature of the threats or the amount of payment demanded.
Past threats have been issued by a group or groups calling themselves AZF.
In July, letters signed by AZF were sent to eight multinational food and cosmetics companies, threatening to poison their products if they did not each pay $1.35 million. However, no evidence of a poison plot was found.
Officials said those threats appeared unrelated to blackmail attempts earlier in 2004 by a group using the same name, which threatened to bomb railway targets unless the government paid $4 million.
AZF happens to be the name of a factory in Toulouse levelled in an explosion in September 2001. No connection has been established in the past.