(corrects spelling of victim's surname, paragraph 2)

* Security guard dies after shooting

* Investigators identify possible suspect

* Suspect linked to anti-government website (Updates with Obama statement in paragraphs 6-7)

WASHINGTON, June 10 (Reuters) - An elderly gunman linked to an anti-Jewish website killed a security guard at the U.S. Holocaust Memorial Museum in Washington on Wednesday and was wounded when guards returned fire, officials said.

The guard, Stephen Tyrone Johns, died at a local hospital after being shot with a rifle, officials said. The museum said it would be closed on Thursday in his honor.

"There are no words to express our grief and shock over these events," the museum said in a statement.

The gunman was in critical condition after the incident, authorities said.

A federal law enforcement official said investigators had identified James W. von Brunn, 88, as the potential suspect and linked him to a website that expresses anti-government and anti-Jewish sentiments.

U.S. President Barack Obama said he was "shocked and saddened" by the shooting.

"This outrageous act reminds us that we must remain vigilant against anti-Semitism and prejudice in all its forms," Obama said, adding that his thoughts and prayers were with the family of the "courageous security guard who stood watch at this place of solemn remembrance."

Washington Mayor Adrian Fenty said the shooting was an isolated incident. "In these days and times you never know when someone is going to grab a gun and use it in an inappropriate way as was done today."

Stephanie Geraghty, 28, who had been visiting the museum, said the shooter appeared to be a white male carrying a silver gun.

"I heard the first shot, it sounded like something had been dropped from the upper stories down," she told Reuters. "The next two came really fast -- bam bam. At that point, everyone took off, chaos, running."

The museum, a memorial to the 6 million Jews killed by Nazis in the Holocaust, is near the National Mall where many of Washington's monuments are located.

"We are horrified by what happened in Washington today. It is especially shocking that this attack took place at a museum designed to prevent violence and remind us of the dangers of hatred and bigotry," Senator Frank Lautenberg said in a statement. (Reporting by Tabassum Zakaria, James Vicini, Christopher Doering and Mari Saito; Editing by Peter Cooney and Paul Simao)

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