But the White House has repeatedly criticised Pelosi's tour during which she has also visited Israel and Lebanon saying it simply provides a photo opportunity for the Syrian leader to exploit.
"We have made it clear to high-ranking officials, whether they be Republicans or Democrats, that going to Syria sends mixed signals," Bush said to reporters at the White House on Tuesday.
The president, who is currently engaged in a political struggle with the Democrat-dominated Congress over funding for the war in Iraq, said the visit could only "lead the Assad government to believe they're part of the mainstream of the international community."
He has consistently accused Syria of sponsoring terrorism and not doing enough to prevent foreign fighters from crossing into Iraq or reining in Hamas and Hezbollah.
Pelosi, on her second visit to the Middle East since becoming House speaker in January, has shrugged off criticism from the White House saying it was a good opportunity to gather facts and build some confidence.
Pelosi and her high-level delegation, were given a red carpet reception, were welcomed at Damascus airport by the Walid al-Moualem, the Syrian foreign minister.