Cheney stopped in London to confer with Blair, America's strongest ally in the terrorism campaign, before a 10-day visit to the Middle East that will include stops in Israel, Turkey and nine Arab countries.
Both Cheney and Blair, at a news conference at 10 Downing Street, noted the six months since the Sept. 11 terror attacks.
"We are not going to turn our backs on Afghanistan. We are not going to let it become a failed state again," Blair said.
Cheney said he had come to Britain because "the president wanted me to check in first with the prime minister."
"I am proud of the role Britain has played," he said.
Cheney said he would discuss both the Afghanistan campaign and next steps in the terror war as he meets with Middle Eastern leaders, but emphasized that he was not announcing decisions on where the next battleground might be.
Cheney is expected to build a case for a tougher policy against Iraq. He said he hopes to talk to leaders of the region about efforts to end the spiraling violence between Israel and the Palestinians.
Cheney and Anthony Zinni, President Bush's special envoy to the Middle East, will be visiting the region at the same time.
While Middle Eastern leaders have indicated the Israeli-Palestinian violence is now the most important crisis in the region, Cheney said the United States has the responsibility to work on both issues — the war against terror and the Israeli-Palestinian crisis.
Cheney was asked about reports over the weekend that the Pentagon has told Congress it is studying a possible use of nuclear weapons against countries, possibly including Iran and Iraq, that may threaten the United States. Despite the fact that the reports have gotten a lot of attention in Europe and the Middle East, Cheney told reporters, "it won't have much effect" on his mission.
With a cadre of military and foreign policy advisers, Cheney flew here from Washington on Sunday aboard the jumbo jet President Bush uses. It was his first overseas trip as vice president.
The United States and Britain have presented a united front on dealing with Iraq, sometimes finding themselves at odds with other top allies.
U.S. and British warplanes still patrol "no-fly" zones in north and south Iraq.
Blair in recent days has toughened his own stance on Iraq. Saddam Hussein "should not underestimate the determination of the international community to prevent him developing and using weapons of mass destruction," Blair wrote last week in a newspaper essay.
While in London, Cheney also planned to visit an information center on the war against terrorism; and the Cabinet War Room Museum, where Prime Minister Winston Churchill helped oversee the allied war effort in World War II.
In addition to Britain, Cheney plans to visit Israel, Turkey, Saudi Arabia, Kuwait, Yemen, Jordan, Egypt, Oman, Qatar, Bahrain and the United Arab Emirates.