NEW YORK —  Attacks by Russian hackers against Georgian Web sites, including one hosted in the United States, continued Tuesday even as Russian President Dmitri Medvedev ordered a halt to hostilities against Georgia.

Tom Burling, acting chief executive of Atlanta-based Web-hosting firm Tulip Systems Inc., said the Web site of the president of Georgia was the target of a flood of traffic from Russia aiming to overwhelm the site.

Burling said bogus traffic outnumbered legitimate traffic 5,000-to-1 at president.gov.ge.

"Literally, our people aren't getting any sleep," Burling said.

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Tulip's firewall was blocking most of the malicious traffic. The site has been periodically inaccessible, though it was working midday Tuesday. Burling said the attacks have been reported to the FBI.

The site was transferred from servers in Georgia, the small nation south of Russia, on Saturday.

Georgian-born Nino Doijashvili, Tulip's chief executive and founder, happened to be in the country on vacation when fighting broke out Thursday.

Doijashvili offered help to the government when it became apparent that Russian hackers were getting the upper hand, shutting down several government and news sites.

The U.S.-based Shadowserver Foundation, which tracks Internet attacks, said they had noticed commands to attack Georgian sites being issued over the weekend to "botnets," or networks of computers that have been surreptitiously subverted by hackers.

The computers are used to send bogus traffic to targeted sites, slowing them or in some cases bringing them down.

The same botnets are also targeting Russian news sites and the Web site of Gary Kasparov, the Russian chess player and political activist, according to Steven Adair at Shadowserver.

On Monday, hackers took over the Web site of Georgia's parliament and replaced it with an image that drew parallels between Georgian president Mikhail Saakashvili and Adolf Hitler, Adair said.