(CNN) -- As Barack Obama targeted John McCain in his attacks Monday, Hillary Clinton told her supporters the race for the Democratic nomination is "nowhere near over."
Obama and McCain blasted each other's views on foreign policy, with McCain slamming Obama's statement that Iran poses a less serious threat to the United States than the Soviet Union did.
Obama shot back during a speech in Billings, Montana, and asked why the presumptive Republican presidential nominee was afraid to talk to Iran.
Obama said it was the "Bush-McCain" war policy in Iraq, not diplomacy, that would make Iran stronger.
"Make no mistake, Iran is the single biggest beneficiary of a war in Iraq that should have never been authorized and should have never been waged," the front-runner for the Democratic presidential nomination said. Watch Obama respond to McCain »
"Thanks to George Bush's policy, Iran is the greatest threat to the United States and Israel and the Middle East for a generation. John McCain wants to double down on that failed policy." Watch what McCain says about Obama »
Meanwhile, Clinton again vowed to keep her campaign alive, telling a crowd in Maysville, Kentucky, "I'm going to make my case until we have a nominee."
"But we're not going to have one today, and we're not going to have one tomorrow, and we're not going to have one the next day.
"This is nowhere near over, none of us is going to have the number of delegates we're going to need to get to the nomination," she argued.
Clinton believes neither candidate will have the necessary 2,210 delegates by the last primary on June 3, the number she says is needed because she argues Michigan's and Florida's delegates must be counted. How CNN political analysts view the primaries »
The Democratic National Committee has set the number of delegates needed at 2,026 after stripping those states of their delegates for scheduling their primaries too early.
The Obama campaign has said that after Oregon and Kentucky's primaries Tuesday, they will have the majority of the pledged delegates.
"Right now, more people have voted for me than have voted for my opponent," said Clinton, a claim muddied by complicated methods to tally voters and Michigan and Florida's questionable status. Watch why Clinton says she's ahead ».
Obama continued to pad his lead Monday, picking up an endorsement from Sen. Robert Byrd, the longest-serving senator in American history.
Byrd, 90, has been a West Virginia senator for nearly 50 years, and is one of the chamber's most vocal critics of the war in Iraq.
Clinton won the primary in West Virginia last week, defeating Obama by a 41-point margin.
Byrd, who is a superdelegate, said his decision came "after a great deal of thought, consideration and prayer over the situation in Iraq."
Obama also picked up an endorsement Monday from Larry Gates, the chairman of the Kansas Democratic Party. Gates is also a superdelegate.
The latest Gallup daily tracking poll suggests Democratic voters are beginning to coalesce around Obama.
He holds a 16-point lead over Clinton in Gallup's daily tracking poll released Monday. He has the support of 55 percent of Democratic and Democratic-leaning voters, while Clinton's support is at 39 percent.
Previously, Obama's largest lead over Clinton was 11 percentage points, in daily tracking polls conducted in mid-May and mid-April, according to Gallup. Before John Edwards' exit from the Democratic nomination race, Clinton held a 20-point lead over Obama in mid-January.
The results are based on a survey of 1,261 Democratic and Democratic-leaning voters using combined data from May 16-18. The poll has a margin of error of plus or minus 3 percentage points.
Clinton and Obama face off Tuesday in Kentucky and Oregon. Clinton holds a comfortable lead in Kentucky, while Obama is the favored candidate in Oregon.
Those two states are expected to do little more than illustrate the divide between Democratic voters in selecting a presidential candidate.
Kentucky is dominated by working-class voters, which has been a source of support for Clinton throughout the prolonged primary season.
Obama's base of support -- young and higher-educated voters -- are better represented in Oregon.
CNN's Alexander Marquardt, Alex Mooney and Martina Stewart contributed to this report.