Bush had angered many Palestinians by lavishing the Jewish state with praise on its 60th anniversary, hailing it as a "homeland for the chosen people".
In the bin Laden message on Sunday, the speaker lashed out at Arab leaders, accusing them of "sacrificing" the Palestinians.
"Each one of us is responsible for the death of our vulnerable people in Gaza where scores have died because of the blockade"
Voice attributed to Osama bin Laden
He said governments such as Egypt had sided with Israel and the West against Islam and that there was "no way to "liberate Palestinian territories without violence".
Israel and Egypt have closed their borders with Gaza since last June, when Hamas took control of the territory following Palestinian factional fighting.
The closure has deepened economic hardship in the already impoverished strip, where 1.4 million Palestinians live.
"Each one of us is responsible for the death of our vulnerable people in Gaza where scores have died because of the blockade," he said.
Sunday's tape was the second message purporting to be from bin Laden in the past week.
An audio tape published on Friday, also attributed to the al-Qaeda chief, condemned Western leaders for celebrating the creation of Israel.
On that tape, the speaker said: "Western leaders' participation with the Jews in this celebration confirms that the West supports this oppressive Jewish occupation of our nation and that they are in the same trench as the Israelis against us."
He said Palestine is at the heart of the Muslim battle with the West, and it was an inspiration to the 19 bombers who carried out the attacks on US cities on September 11, 2001.
"We will continue, God permitting, the fight against the Israelis and their allies ... and will not give up a single inch of Palestine as long as there is one true Muslim on earth," he said.
Laura Mansfield, whose website monitors purported al-Qaeda messages, said bin Laden appeared to be changing his emphasis.
She said on her website: "In his initial messages, bin Laden's focus was on the removal of US forces from [Saudi Arabia] but in recent years he has more closely wedded himself to the Palestinian issue."