Five of France's leading rightwing politicians, including President Nicolas Sarkozy and three of his cabinet ministers, have been sent death threats accompanied by 9mm-calibre bullets, police said today .

The justice minister, Rachida Dati, the interior minister, Michele Alliot-Marie, and the culture minister, Christine Albanel, had all received anonymous packages in the past week, their respective offices confirmed. Contradicting an earlier denial by Sarkozy's spokesman, the police said the president had also been targeted, along with the former prime minister and mayor of Bordeaux, Alain Juppé.

"You think you control our lives – well, no, it's us who control yours and those of your family and friends," the letters were reported to have said. Typed by computer over two pages and in brown paper envelopes, some of the messages described the recipients as the legislators of "liberty-crushing" and "fascist" laws. Police said others referred to the politicians as "dead men walking".

It was not clear whether the sender or senders had any specific political agenda or complaint, but investigators in Paris's counter-terrorism police department said they thought it probable the threats were the work of a mentally unstable person.

At the end of last week, copies of the letters and individual bullets were also sent to two MPs in Sarkozy's ruling UMP party: Jacques Blanc, mayor of La Canourgue, and Raymond Couderc, senator-mayor of the town of Béziers.

Juppé, who was prime minister for two years under Jacques Chirac, said he had lodged an official complaint with the police but felt "absolutely serene" despite the menacing tone of the packages. "These are the risks of the job," he said. "If you start reading anonymous letters when you're in politics, you'll never stop. You have to step back a bit."

Referring to a German citizen who was found to have been sending him death threats several years ago, Juppé added: "It's not the first time and it won't be the last."