Making his national political debut, Republican star Arnold Schwarzenegger told delegates gathered at the party's convention in New York City he's not afraid to throw the weight of his endorsement behind George W. Bush.

"I believe in this president," Schwarzenegger told the cheering crowd at Madison Square Garden.

Then, in a reference to the Terminator character for which he's so famous, the bodybuilder-turned-actor and now politician declared, "America is back."

"Back from the attack on our homeland -- back from the attack on our economy, back from the attack on our way of life," he said, crediting Bush for that comeback.

Besides playing on his Hollywood star status, Austrian-born Schwarzenegger also used his speech to touch on an issue that has divided his party -- immigration.

"In this country, it doesn't make any difference where you were born. It doesn't make any difference who your parents were. ... America gave me opportunities and my immigrant dreams came true," he said.

"I want other people to get the same chances I did, the same opportunities."

Schwarzenegger's co-star on Tuesday night, First Lady Laura Bush, used her time in the spotlight to heap praise on her president husband.

After a satellite video introduction by her husband, who was, in turn, introduced by his twin daughters, Laura Bush wasted little time.

"I want to talk about the issue that I believe is most important for my own daughters, for all our families, and for our future: George's work to protect our country and defeat terror so that all children can grow up in a more peaceful world," she said.

As a result of that work, she added, some 50 million people have found freedom in the past four years.

While Schwarzenegger and Bush were both overwhelmingly positive in their remarks, building up the president, many on the convention floor are relishing the chance to tear John Kerry down.

For example, many are sporting so-called purple heart bandages that they say make mock of Kerry's disputed Vietnam war record.

"I woke up this morning and I cut myself so I awarded myself a purple heart," one delegate told CTV News.

Although Kerry is staying out of sight during the convention, Democratic officials are outraged their nominee is under such relentless attack.

Reporting from New York City, CTV's Alan Fryer says some are beginning to question the wisdom of Kerry's strategy at his party convention last month -- steering clear of negative attacks on his rival -- given the drubbing he's taking now.

They may have good reason to second-guess, given the fact Americans appear to be warming to the Republican message. A poll released by the Washington Post on Tuesday showed Bush and his Democratic rival John Kerry in a dead heat. Although both showed around 48 per cent support, the poll suggested Bush is edging ahead on national security issues.

Perhaps with that in mind, George Bush was careful to tell supporters he foresees America one day winning the war on terror.

"We meet today in a time of war for our country, a war we did not start yet one that we will win," he told an American Legion convention in Tennessee.

The day before, in a pre-taped interview aired on The Today Show, Bush said he doubted such a victory was possible.

"I don't think you can win it," Bush said. "But I think you can create the conditions that those who use terror as a tool are less acceptable in parts of the world."

Meanwhile, police said they were being kept busy maintaining order in New York City. More than 500 people had been arrested since the weekend, police said, including a group of fourteen who blocked morning rush hour traffic on Wall Street, and a 21-year-old Yale student who found his way into a restricted area near Vice President Dick Cheney's convention booth. Security personnel said that, aside from shouting anti-war statements, the young protester posed no threat.

Bush is expected to arrive in New York on Wednesday, the day before he is slated to accept the party nomination. After that, he will head for the key battleground states of Pennsylvania and Ohio.