Blair's remarks came as eight B-52 bombers armed with 20 cruise missiles each flew out of their base in Gloucestershire, England, Wednesday morning, to attack Serb air defenses.
Western allies, however, said the door was open for Milosevic to accept a plan for peace in Kosovo that he has rejected.
"One phone call from Milosevic would be enough. That is possible at any time and the whole military process will be stopped," German Foreign Minister Joschka Fisher said at a European Union summit in Berlin.
U.N. Secretary-General Kofi Annan said Wednesday he understood why force might have had to be used in Kosovo but emphasized that the U.N. Security Council needed to be involved in any decision to use it.
Military forces were placed on alert and borders were closely watched as nations surrounding Yugoslavia prepared for fallout from the NATO air strikes.
The most immediate worry appeared to be the possibility of refugees fleeing Serbia and its predominantly ethnic Albanian province of Kosovo, where separatists have fought Serb-led Yugoslav forces for more than a year.
Some leaders also echoed President Clinton's concern that the entire region was at risk.
"The fire in Kosovo could engulf the whole Balkans," said Turkish Prime Minister Bulent Ecevit.
In Albania, which took the brunt of last year's exodus of ethnic Albanians from Kosovo, additional soldiers were sent to the impoverished and rugged northern border region. Bunkers were prepared in case of cross-border retaliation by Yugoslavia.
No figures on Albanian troop strength were given, but Albanian Prime Minister Pandeli Majko said the deployment in the area was the "largest... since World War II."
Shelters and camps were set up in northern Albania to handle more refugees, authorities said. Hospitals were stocked with extra supplies.
In neighboring Macedonia, where more than 10,000 NATO troops are stationed, authorities reopened the borders to Yugoslav citizens after closing them Tuesday.
Macedonia said it can't handle more refugees. But there are also deep concerns about unrest spreading to the nation's own ethnic Albanian enclave of Tetovo.
The NATO contingent in Macedonia was assembled for a possible peacekeeping mission in Kosovo before that proposal was rejected by Yugoslav President Slobodan Milosevic. The multinational force isn't expected to play any role in the NATO strikes.
"Our country won't allow its territory to be used in an attack on any neighboring country, including Yugoslavia, and I think NATO will accept this," Macedonian Premier Ljubco Georgievski said Tuesday.
Greece, too, opposes military action against Serbs, who share the same Orthodox faith and are traditional allis.
Increased security measures were imposed along Greece's borders with Macedonia and Albania.
"We need calm," appealed Greek Premier Costas Simitis.
Some political commentators have suggested that Greek authorities are keeping close tabs on ultranationalist and anti-American groups sympathetic to the Serbs. About 3,000 people took part in a Communist-organized march through central Athens to denounce NATO and the United States.
In Bulgaria and Hungary, which have opened their air space to NATO warplanes, there were mixed views over the chances of retaliation from neighboring Yugoslavia.
NATO Secretary-General Javier Solana tried to calm fearful officials in Bulgaria, which isn't a member of the alliance. Solana said Bulgaria's "security is of direct and material concern to NATO."
Hungary, a new NATO member, is "not in any danger," assured Prime Minister Viktor Orban.
The Hungarian parliament voted late Wednesday to let NATO use Hungarian military airfields in its campaign against Yugoslavia.
In Romania, which also borders Yugoslavia but isn't a NATO member, Defense Minister Victor Babiuc said the nation supports the military alliance.
Chief of Staff Constantin Degeratu said Romania had taken "all necessary measures," but refused to give details.
In Bosnia-Herzegovina, where ethnic Croats and Muslims fought Serb-backed forces until a U.S.-brokered peace deal in 1995, the U.S. State Department urged all U.S. citizens to leave the Republika Srpska, the Bosnian Serb half of the country.
Outside the region, some nations also were taking precautions.
In Italy, anti-aircraft batteries were moved into position along the southeastern coast. Italian officials think Italy is out of range of the Serbs' capacity to retaliate. However, U.S. warships near Italy in the Adriatic Sea were expected to play an early role when air strikes were called.
At the Vatican, Pope John Paul II offered the "gift of peace" to Kosovo during his Wednesday audience.
The Kremlin said Russian President Boris Yeltsin was "deeply shocked" by NATO bombing attacks on Yugoslavia.
Yeltsin then made an "appeal to the world" on Russian television, asking people around the globe to "join Russia in its outrage. From our side, we are trying to do what we can, but we can't do anythingÂ… Let's stop Clinton. Let's help him not commit this tragic step."
Russia also called for an emergency meeting of the U.N. Security Council, and withdrew its representative to NATO.
Fellow Slavic nations Belarus and Ukraine also voiced support on Wednesday for Yugoslavia.
Elsewhere around the world, China announced its opposition to the air strikes, saying the Kosovo crisis was an internal affair.