By Lisa Barrington

BEIRUT (Reuters) - The family of American journalist Marie Colvin, who died in Syria in 2012, has filed a wrongful death lawsuit in a U.S. court, accusing the Syrian government of deliberately killing her.

Colvin and French photographer Remi Ochlik were killed in the besieged Syrian city of Homs in 2012 while reporting on the Syrian conflict, now in its sixth year.

The lawsuit, filed in Washington on Saturday and seen by Reuters, said Syrian officials deliberately targeted rockets against a makeshift broadcast studio where Colvin and other reporters were living and working.

The Syrian Foreign Ministry, the target of the lawsuit, could not immediately be reached for comment. The Syrian ambassador to the United Nations could not immediately be reached for comment either.

The suit alleges the attack was part of a plan orchestrated at the highest levels of the Syrian government to silence local and international media "as part of its effort to crush political opposition".

The lawsuit included as evidence a copy of an August 2011 fax which it alleges was sent from Syria's National Security Bureau instructing security bodies to launch military and intelligence campaigns against "those who tarnish the image of Syria in foreign media and international organizations".

Foreign governments are typically immune from U.S. civil lawsuits, but there are exceptions for countries designated by the State Department as sponsors of terrorism. Syria is currently one of three countries on the list, with Iran and Sudan.

Lawyers who have brought civil lawsuits against those governments say they typically do not respond, resulting in default judgments for plaintiffs. The bigger challenge is usually enforcing the judgments and collecting damages, says Gary Osen, a New Jersey lawyer currently suing Iran.

Osen said it was usually hard to identify seizable U.S. assets of those governments subject to terrorism suits, who often operate behind layers of intermediaries. "It could take you decades to find out they own an office building in downtown Boston or somewhere," he said.

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The family's lawsuit is seeking monetary damages but did not specify an amount.

"This case is about carrying on Marie's work," plaintiff Cathleen Colvin, Marie Colvin's sister, said.

"We are seeking truth and justice not just for her, but for thousands of innocent Syrians tortured or killed under the Assad dictatorship," she said in a statement released by U.S. human rights group the Center for Justice and Accountability (CJA) which filed the case for the Colvin family.

Advocacy group Reporters Without Borders said it supported the lawsuit.

The group's secretary-general, Christophe Deloire, said Reporters Without Borders "hopes these efforts will help to expose the truth, namely that these journalists were deliberately targeted and killed because they were providing information about the Syrian army's crimes against civilians."

A murder and attempted murder investigation was launched in France in 2012 into the death of Ochlik and wounding of another journalist, Edith Bouvier, in the same attack.

Reporters Without Borders, as an interested party in the case, said it will submit the Colvin family's U.S. lawsuit to the judge in charge of the French investigation on Monday.

Colvin and Ochlik were both prize-winning reporters of wars in the Middle East, Asia and elsewhere. The Britain-based Colvin, who lost an eye while working in Sri Lanka in 2001, was working for the Sunday Times at the time of her death.

(Reporting by Lisa Barrington; Additional reporting by Anthony Lin and Nate Raymond in New York; Editing by Adrian Croft and Sandra Maler)