While Bush said Bin Ladin's threats would not intimidate Americans, Kerry renewed his vow to hunt down the al-Qaida chief.
"Let me make this very clear. Americans will not be intimidated or influenced by an enemy of our country," Bush said shortly after Aljazeera aired the new Bin Ladin video.
"I want to say to the American people that we are at war with these terrorists, and I am confident that we will prevail," he said.
In a statement, Kerry said he will do whatever it takes to capture or kill "terrorists".
Usama Bin Ladin threatened US
with more attacks in the tape
"In response to this tape of Usama bin Ladin, let me just make it clear, crystal clear, as Americans we are united in our determination to hunt down and destroy Usama bin Ladin and the terrorists," Kerry said.
"They are barbarians, I will stop at absolutely nothing to hunt down, capture or kill the terrorists wherever they are, whatever it takes," he said on the tarmac at West Palm Beach airport.
The White House meanwhile said there was no immediate change in the US terrorism alert level following the airing of bin Ladin's latest video.
"There is no change in it at this time but it's something we analyse all the time," White House spokesman Scott McClellan said. "We are on a heightened state of awareness already."