Sen. Bob Graham (D-Fla.) said yesterday he is considering a 2004 presidential bid, outlining a goal of extending unemployment benefits, limiting President Bush's tax cut and moving the country's international focus from war with Iraq to the battle against al Qaeda.

"We ought to be focusing on a broader range of issues than just tax cuts," Graham, 66, said in an interview. "An extension of unemployment benefits is needed immediately, along with relief to the states whose economic problems are going to create job losses, fraying the security net for those in greatest need."

Graham, in his third Senate term and up for reelection in 2004, said he also would press policies to build and restore "America's transportation and environmental infrastructure." He said he would oppose a centerpiece of the Bush agenda, which is to make the 2001 tax cut permanent. The GOP plan, he said, disproportionately helps the wealthy. He said he would support a temporary cut, possibly eliminating the payroll tax on the first $10,000 of income so that it would primarily help those in the lowest tax brackets.

Graham first spoke of a possible White House bid during and immediately after appearing on a Haitian American radio show in Miami. "We're facing unprecedented problems in terms of our domestic economy, in terms of our international relations, particularly the war on terrorism and Iraq," he told reporters there. He said he was "not satisfied with the direction we are being led today," and he is "considering what I think could be my contribution toward a new direction for America."

Graham voted against the resolution granting Bush authority to initiate war against Iraqi President Saddam Hussein's regime. He said he opposed the resolution "not because our nation has nothing to fear from Hussein but because I am convinced that the resolution misstates our national priorities in a dangerous way. . . . Right now the most urgent threats to our security are posed by the shadowy networks of international terrorist organizations that have the capabilities to repeat the tragedy of September 11 -- not Saddam Hussein."

The impromptu character of Graham's comments made it difficult to assess the degree to which he planned them in advance. He said he plans to make his decision over the "next several weeks."

On paper, Graham -- elected to the Senate in 1986 after eight years as Florida governor -- would bring solid credentials to a fight for the nomination. He is one of the most popular politicians in Florida, a key swing state and a strong base for raising money. He has held elected office there for 36 years, surviving as the state shifted from solidly Democratic to mostly Republican to the 50-50 balance that transfixed the nation in the 2000 presidential count. Graham has prospered, in part, by taking liberal stands on such issues as the environment and abortion, while backing capital punishment and asserting himself as a deficit hawk.

The ranking Democrat on the Senate Select Committee on Intelligence, Graham has been a party spokesman regarding terrorism and Iraq. He made the short list of potential running mates for the party's last three nominees: Michael S. Dukakis, Bill Clinton and Al Gore.

Under Florida law, he would have to forgo a bid for a fourth Senate term if he runs for president in 2004.

Graham is the half-brother of the late Phil Graham, a publisher of The Washington Post.

The field of potential and announced Democratic presidential candidates includes Sens. Thomas A. Daschle (S.D.), John F. Kerry (Mass.), Joseph I. Lieberman (Conn.) and John Edwards (N.C.), outgoing House Minority Leader Richard A. Gephardt (Mo.), Vermont Gov. Howard Dean and black activist Al Sharpton of New York.

Sen. Bob Graham (D-Fla.) said extending unemployment benefits would be on his agenda if he runs for president in 2004.