President George W. Bush talked with his top national security adviser on Saturday about the world's reaction to the hanging of Saddam Hussein — an execution the president called a milestone on Iraq's road to democracy.

Bush cautioned that Hussein's death will not halt the bloodshed and political discord splitting the country. He warned of more challenges ahead for U.S. troops.

"Many difficult choices and further sacrifices lie ahead," he said in a statement released Friday night from his Texas ranch. "Yet the safety and security of the American people require that we not relent in ensuring that Iraq's young democracy continues to progress."

The threat of violence comes at a time when Bush is completing his weeks-long effort to change U.S. policy in Iraq.

The president's statement had a sober, measured tone that contrasted with his offhand remark after U.S. troops found the deposed Iraqi dictator in an underground hideout in 2003.

"Good riddance," Bush said then. "The world is better off without you, Mr. Saddam Hussein."

Bush said Hussein received a fair trial — "the kind of justice he denied the victims of his brutal regime." He said the trial, which ended with Saddam being sentenced to death, was a testament to the Iraqi people's resolve to move beyond decades of oppression and create a society governed by the rule of law.

"Fair trials were unimaginable under Saddam Hussein's tyrannical rule," Bush said.

Saddam's hanging comes at the end of a difficult year for Iraqis and for U.S. troops, he said. The U.S. death toll is nearing 3,000, and December is going down as one of the deadliest for American troops since the U.S.-led invasion in March 2003.

"Bringing Saddam Hussein to justice will not end the violence in Iraq, but it is an important milestone on Iraq's course to becoming a democracy that can govern, sustain, and defend itself, and be an ally in the war on terror," he said.

Bush was asleep when Saddam was executed for the killings of 148 Shiite Muslims from an Iraqi town where assassins tried to kill him in 1982. On Monday, Iraq's highest court rejected Saddam's appeal of the sentence and ordered him put to death.

"The president concluded his day knowing that the final phase of bringing Saddam Hussein to justice was under way," deputy White House press secretary Scott Stanzel said.

At 6:15 p.m. CST Friday, National Security Adviser Stephen Hadley briefed Bush on the procedures for the execution, and told him it would take place in the next few hours. Hadley had been in touch with U.S. Ambassador to Iraq, Zalmay Khalilzad, who had been in contact with Iraqi Prime Minister Nouri al-Maliki.

"The president was pleased with the culmination of the Iraqi judicial process and that justice was done," White House spokesman David Almacy said, describing Bush's reaction to learning that the execution was close to being carried out.

Bush arose shortly before 5 a.m. CST on Saturday and had a 10-minute phone call about an hour later with Hadley to discuss world reaction to the execution, Almacy said. Bush received his daily intelligence briefing and plans to spend the rest of the day cutting cedar on his ranch, taking a bike ride, spending time with first lady Laura Bush and pondering his next steps in Iraq.

American sentiment about the war has changed dramatically since the spring of 2003 when jubilant crowds of Iraqis toppled a 40-foot statue of the dictator and a disheveled Saddam, in U.S. custody months later, was seen on television being examined by a doctor who probed his mouth with a tongue depressor.

Then, Saddam's capture boosted Bush's political stature, following months of rising casualties and the manhunt for the former Iraqi dictator, which had damaged U.S. prestige and claims of progress in Iraq.

Now, unrelenting violence and a U.S. death toll nearing 3,000 has sent Bush's approval ratings on the war plummeting to their lowest levels. Seventy-one percent disapprove of his management of the war; almost two-thirds doubt that a stable, democratic government will ever be established in Iraq, according to early December AP-Ipsos polling.

As Saddam's execution drew near, his lawyers lost an appeal in a U.S. court to try to stave it off.

In a 21-page request filed Friday, Saddam's attorneys argued that because he also faced a civil lawsuit in Washington, he had rights as a civil defendant that would be violated if he is executed.

But U.S. District Judge Colleen Kollar-Kotelly, who heard arguments from attorneys by phone, rejected the challenge Friday night, saying U.S. courts do not have jurisdiction to interfere in another country's judicial process.

In Iraq, U.S. forces were ready for any escalation of violence, Pentagon spokesman Bryan Whitman said hours before Saddam was hanged.

Closer to home, the FBI and the Homeland Security Department warned Americans to be vigilant about the possibility of a terror attack. The advisory sent to local law enforcement agencies did not cite a specific threat.

Members of Congress welcomed the news of Saddam's death.

"Iraq has closed one of the darkest chapters in its history and rid the world of a tyrant," said Democratic Sen. Joseph Biden of Delaware, incoming chairman of the Senate Foreign Relations Committee.

The Republican leader-elect of the Senate, Mitch McConnell of Kentucky, said Saddam finally had met justice.

"The free people of Iraq must now go forward together to build a unified nation, and leave behind sectarian divisions."