Bush issued the call at a hastily arranged White House news conference at which he also acknowledged the increasing bloodshed in Iraq, and said he expected the killing would accelerate in the coming months.
Bush didn't say what further sanctions he wanted, but said his administration will work with U.S. allies to make sure any new measures are implemented.
Secretary of State Condoleezza Rice will work with European governments, Bush said, adding that persuading Russia and China to agree to more sanctions might be difficult.
Those two countries are permanent members of the UN Security Council and have veto power on any resolution.
"We will work with our European partners to develop further sanctions," Bush said. "And, of course, I will discuss this issue with [Russian President] Vladimir Putin, as well as [Chinese] President Hu Jintao. The first thing that these leaders have got to understand is that an Iran with a nuclear weapon would be incredibly destabilizing for the world."
The UN's nuclear agency, the International Atomic Energy Agency (IAEA) reported on May 23 that Iran is defying the world body by accelerating uranium enrichment.
Washington responded by sending nine warships -- including two aircraft carriers -- into the Persian Gulf to conduct war games, in a show of military might.
Iran also has raised the tension level recently by detaining or confiscating the passports of people with dual Iranian and U.S. citizenship, including Radio Farda reporter Parnaz Azima and American-Iranian scholar Haleh Esfandiari.
The United States could discuss the detentions and the nuclear program with Iranian government officials on May 28 at a meeting in Baghdad between U.S. Ambassador to Iraq Ryan Crocker and his Iranian counterpart, Hasan Kazemi-Qomi. The meeting was called to discuss ways Iran can help stabilize Iraq.
Expecting A Tough Summer In Iraq
U.S. officials say it should be clear by September whether Bush's so-called surge strategy of sending more troops to fortify Baghdad has worked.
At today's news conference, a reporter asked Bush if that means Al-Qaeda in Iraq and sectarian militias will increase their attacks during the summer to influence U.S. public opinion.
Bush acknowledged that the summer will be a test of his new war policy.
"This summer is going to be a critical time for the new strategy," Bush said. "The last of five reinforcement brigades we are sending to Iraq is scheduled to arrive in Baghdad by mid-June. As these reinforcements carry out their missions, the enemies of a free Iraq, including Al-Qaeda and illegal militias, will continue to bomb and murder in an attempt to stop us. We're going to expect heavy fighting in the weeks and months. We can expect more American and Iraqi casualties."
The U.S. president also called on the Iraqi government of Prime Minister Nuri al-Maliki to improve its performance in providing its own security. He noted that this was a key recommendation of the Iraq Study Group -- a bipartisan panel of U.S. foreign-policy leaders -- that issued its report in December.
And Bush referred to the war-funding bill being considered now by Congress that includes performance benchmarks for the Iraqi government.
"The Iraq Study Group recommended that we hold the Iraqi government to the series of benchmarks for improved security, political reconciliation, and governance that the Iraqis have set for themselves," Bush said. "I agree. So does the Congress. And the bill reflects that recommendation. These benchmarks provide both the Iraqi government and the American people with a clear road map on the way forward. Meeting these benchmarks will be difficult. It's going to be hard work for this young government."
Three weeks ago, Bush vetoed a measure to fund the wars in Iraq and Afghanistan. That bill, however, also would have required him to begin troop withdrawals from Iraq this autumn.
Democrats, who control Congress, stripped that requirement from the current legislation after negotiations with the White House. They acknowledged that they couldn't find enough votes to override another veto.