Bush will arrive in Israel on Wednesday and spend much of Thursday in the occupied West Bank, including a stop at Abbas's headquarters in Ramallah and in Bethlehem.
By skipping the Hamas-controlled Gaza Strip, Bush will not see school pupils and their parents and teachers demonstrating against the ongoing Israeli siege, according to Al Jazeera's Mike Hanna.
He will not see the shortage of medical supplies, fuel and power due to Israeli restrictions, Hanna said.
On Tuesday, about 3,000 supporters of the Islamic Jihad marched in the Gaza Strip, chanting: "Bush, you are the great devil."
The protesters also shouted "Death to America", "Death to Israel", and burned American and Israeli flags.
The march was also against the ongoing Israeli siege of Gaza.
Participants carried 62 coffins symbolising those who have died because they have been unable to leave the area for medical treatment.
Hamas is to hold an anti-Bush rally on Wednesday, with a four-metre-long banner denouncing Bush as a "war criminal" serving as the centrepiece.
For their part, Israeli forces will seal off the West Bank completely for the duration of the visit, a military spokesman said on Tuesday.
"The lockdown will come into force at midnight local time (2200 GMT) on Tuesday and will be lifted on Saturday at a time that has yet to be determined," the spokesman said.
US snipers will take up positions on Ramallah rooftops and local traffic will be barred from some downtown districts, Palestinian officials said.
Before dawn on Tuesday, a pair of rockets struck a northern Israeli town, allegedly fired from Lebanon, without causing much damage or any injuries.
No one took responsibility for the attack, which was just the second such incident since the end of the 2006 Israel-Hezbollah war.
Speaking to Al Jazeera on Monday, Mark Regev, spokesman for Olmert, had defended the Israeli military operations in the Palestinian territories.
He said: "We've got a situation where the Palestinian security services need to get their act together, need to rebuild, need to be retrained. They need to have their capabilities improved.
"That's not just the Israeli position, that's the position of the Arab world, the Europeans, of everyone who has following this process. And so I will say publicly and clearly: when Palestinian security is ready to meet the challenges, then Israeli security will not have any need to act."
On the opposite side, Mustafa al-Barghouti, the head of the Palestinian National Initiative, blamed Israel for the deadlock at a news conference on Tuesday.