By Krisztina Than and Marton Dunai

BUDAPEST (Reuters) - Around 2,000 Hungarians protested in Budapest on Saturday against the closure of the country's leading leftist newspaper Nepszabadsag, saying press freedom was under threat.

Owner Mediaworks said on Saturday it had suspended the newspaper and its employees after the publication piled up significant losses despite cost cuts. It said it would revamp the organization.

But civil rights groups said the newspaper had been shut down because it had published stories critical of right-wing Prime Minister Viktor Orban's government and called for the demonstration in front of the parliament building.

"Today one of the last opposition newspapers was simply silenced," the civil rights groups said on Facebook.

The radical nationalist Jobbik opposition party blamed Orban for the closure, saying his Fidesz party wanted to control the entire Hungarian media.

"Sudden closure of Nepszabadsag sets a worrying precedent. I stand in solidarity with Hungarians protesting today," European Parliament President Martin Schulz ‏tweeted.

Fidesz said it regarded the closure as a "reasonable business decision" by the publisher.

Mediaworks, owned by Austrian firm Vienna Capital Partners, said it was working on a new business model for Nepszabadsag (People's Freedom), which has been in publication since November 1956.

"In order to achieve and concentrate fully on this priority task, all operations of Nepszabadsag (including print and online) will as of today be suspended until the new form is decided and can be implemented," it said on the paper's website nol.hu.

Employees, who received letters on Saturday informing them of Mediawork's decision, said the closure had come as a shock, and editor Andras Muranyi told ATV that talks with the company were under way.

"Our first thought is that this is a coup. We will soon come back with more," Nepszabadsag said in an editorial on its Facebook page.

In its final edition on Saturday, the newspaper reported the latest in its articles on a minister in Orban's government using a helicopter to fly to a wedding.

"I don't usually attend demonstrations because my blood pressure goes up but now I felt I had to come.. It is a shameful thing that has been done here," Erzsebet Kovacs, one of the demonstrators, said.

"The free media is being suffocated," another demonstrator Tamas Waldmann said.

Some protesters burned copies of the pro-government daily Magyar Idok at the rally, website Index.hu reported.

Government spokesman Zoltan Kovacs said the government did not deal with developments in the media industry. "In Hungary press freedom is doing well," he added.

(Additional reporting by Krisztina Fenyo; editing by Susan Thomas)