Their White House meeting on Thursday, to be followed by a joint press conference, is the first between Bush and Abbas since Israel evacuated the Gaza Strip last month after 38 years of occupation.
Israel, however, still maintains land, sea and air control over the Strip.
Washington sees the Gaza pullout as a chance to revive a US-backed peace "road map" that envisions Palestinian statehood.
The Bush-Abbas talks are taking place after Israel cut ties with the Palestinians in response to the killing on Sunday of three Jewish settlers.
Israel killed a resistance fighter the same day, froze security contacts and restored some road blocks it had lifted.
"There is more that the Palestinian leadership can do to end violence and dismantle terrorist organisations.
"It is important that the Palestinian leadership continues to take steps to put in place law and order in Gaza," said White House spokesman Scott McClellan.
Palestinian officials say Abbas will tell Bush that not only are the hopes, raised by the Gaza pullout, now in doubt, but so too is Bush's own vision of a viable Palestinian state one day in the West Bank and Gaza Strip.
Abbas will focus on the separation
barrier and settlement expansion
At the top of the list of Abbas's wishes is pressure on Israel to halt settlement expansion in the West Bank and construction of the barrier there which Israel says keeps out bombers but Palestinians call a land grab.
Abbas also wants to end an argument over border crossings that has left Gaza largely sealed up since the Israelis withdrew.
He wants Israel to agree to open the Gaza sea and airports and to allow a free land route to the West Bank.