"I don't want to prejudge the report that's coming out," Bush told reporters Wednesday.
Nevertheless, he said, "we have a lot of expectations for Syria beyond just the Mehlis report."
After a session with Poland's retiring president Aleksander Kwasniewski at the White House, Bush was asked about the consequences for Syria should the Mehlis report link its officials to Hariri's death. The U.N. Security Council is to discuss the report Oct. 25.
"I think it's very important for Syria to understand that the free world respects Lebanese democracy and expects Syria to honor that democracy," Bush said.
"You know, it's one thing to have been asked to remove troops and all intelligence services. Now the world wants for, expects Syria to honor the democracy in the country of Lebanon."
The question arose because of the suicide in Damascus Wednesday of Interior Minister Ghazi Kanaan, 63, who was Syria's security chief in Lebanon for almost 20 years and reportedly was questioned by Mehlis.
While awaiting the Mehlis report, Bush said, "we're continuing to work with friends and allies to send a clear message to the Assad government there are expectations involved for countries that want to be accepted in the international community."
The second demand the United States has of Syria, Bush said, is "to do everything in her power to shut down the transshipment of suiciders and killers into Iraq. We expect Syria to be a good neighbor to Iraq."
U.S. officials say many of the foreigners who have joined the Iraq insurgency at least pass through Syria en route to the Iraqi battleground, even flying into the Damascus airport before making the journey east. Syrian President Bashar Assad's government contends its border is too permeable to seal effectively.
Bush also said Syria must not "agitate killers in the Palestinian territory."
"We're making good progress toward peace in the Holy Land," he said, "but one of the areas of concern is that foreign countries, such as Syria, might try to disrupt the peace process through encouraging terrorist activity."
Several Palestinian groups have headquarters in Damascus or elsewhere in Syria.(AP-Naharnet)