Spanish Interior Minister Fernando Grande-Marlaska and the leader of the left-wing Unidas Podemos party Pablo Iglesias have received death threat letters, Iglesias said.
"Your wife, your parents and you are sentenced to the capital punishment, your time is running out," the anonymous letter said, according to a picture posted by former deputy Prime Minister Iglesias on Twitter.
He also posted a picture of four bullets which he said had come in the envelope.
Iglesias said the interior ministry had told him it considered the threats serious and police were investigating.
"I hope some arrests will happen," he told the state broadcaster TVE.
The interior minister and the head of the Guardia Civil police force received similar letters, Iglesias said. He did not say if bullets were enclosed.
Grande-Marlaska did not make any official comment.
Pony-tailed Iglesias has emerged as one of Spain's main political leaders after Podemos, created in 2014 and later renamed Unidas Podemos, became the main group on the far-left.
The party allied with centre-left Socialist Party in January 2020 to form the first coalition government since the return of democracy in Spain in the 1970s.
Iglesias was Social Rights Minister and deputy Prime Minister until March, when he quit to run in regional elections in Madrid, scheduled on May 4.
Politicians from the government coalition, including Prime Minister Pedro Sanchez, and from the main parties have expressed solidarity with Iglesias and Marlaska.
Far-right Vox party's candidate for the Madrid elections, Rocio Monasterio, said she condemned any violence, though she said she believed little of what Iglesias ever says.