On polling day on Sunday, the regional government's computer systems received 60,000 times more hits than usual in "hard, organised cybernetic attacks",
said its president Artur Mas.
"They tried to take down the Catalan government's computer systems."
He was speaking to reporters in his first public address since Sunday's polls, in which 2.3 million people turned out to vote on whether the rich region should break away from Spain.
Spain's Prime Minister Mariano Rajoy fiercely opposed the vote and has not reacted since the polls on Sunday, in which 1.86 million people voted for independence out of a total eligible voting population estimated in the range of 5.4 million and 6 million.
He is expected to appear in public on Wednesday afternoon, however, in a press conference not previously scheduled. He is expected to make a public announcement to silence critics who have accused him of inaction since Sunday's vote, Spanish daily El País reported.
Mas reached out to Rajoy on Tuesday, saying it was time Madrid entered into a "permanent dialogue" with Catalonia.
He said he had written to Rajoy inviting him "to set the conditions for a dialogue that is permanent and as constructive as possible".
The ultimate aim of the dialogue is to hold "a definitive and politically binding consultation" vote, Mas added.
"The issue we are faced with can only be resolved at the top political level."
Describing the cyberattack, Mas said that hits on his government's computer systems multiplied 20,000 times on Saturday and 60,000 on Sunday.
"Never before had we suffered an organized attack of such scale and characteristics," he said, adding that the assault had threatened to disrupt medical services.
"We suspect that it could not just be a few amateur hackers or Twitter users who organised such a thing," he said. "We are examining another possibility."
The leading Catalan pro-independence lobby ANC said hundreds of its members who worked as volunteers running Sunday's vote had their telephones jammed.
One ANC volunteer during the vote showed news agency AFP how his telephone was receiving unsolicited automated calls every 30 seconds for hours.
Mas said he would hold talks over the coming weeks with Catalan political parties that support the right to vote on independence, to plan his next steps.
Spain's government on Tuesday rejected Spain's government Tuesday rejected Catalonia's calls for self-determination.
"The right to self-determination... is not possible, neither under our constitution nor in any of the other democracies around us," Deputy Prime Minister Soraya Sáenz de Santamaría told parliament.