Suleiman Hadad, a Syrian MP, said: "President Bush is no longer acceptable worldwide."
Iranian state television quoted commentators saying that Bush's strategy in the Middle East, especially in Iraq, and in Afghanistan were the main reasons for his party's failure. It also blamed financial corruption in the US.
Some Arabs dismissed the results because they saw little difference between Democrats and Republicans on issues such as Americn support for Israel.
Yousef Abu Hijra, who runs a mobile phone shop in Amman, Jordan, said: "I don't believe there will be any change at all in US policy. There's no difference between the two parties."
In Israel, too, some hold that view.
"This country [Israel] is very important for them. From my point of view, they will do anything to protect Israel, no matter which party"
Rami Bengur, an Israeli video shop owner
Rami Bengur, an Israeli video shop owner, said: "What I think is that for Israel, it makes no difference which party will take the power.
"This country is very important for them. From my point of view, they will do anything to protect Israel, no matter which party."
But Jacob Kay, a web designer, said he was worried that the Democrats would change policy towards Iran because "the supporters of Israel and freedom in the Middle East actually tend to be Republicans".
For many Arabs, the war in Iraq stands out as the defining event of the Bush administration.
Mustafa Ahmed Orabi, an office manager in Amman, said he hoped for change because Bush "has been more aggressive - even more than past US presidents".
In Baghdad, the US ambassador sought to reassure Iraqis that American policy would not alter radically. But some Iraqis said they hoped that the Democrats would be able to effect some changes.
Suheil Jabar, a Shia Muslim engineer, said: "I hope this will change the Bush policy in the Islamic world and especially in Iraq. We hope American foreign policy will change and that living conditions in Iraq will improve."
A Kuwaiti political analyst, Abdul-Ridha Aseeri, described the Democrats' gains as a "normal reaction" to the president's "failed" policies in Iraq. Kuwait was among the few Arab countries where support for the war was strong when it began in 2003.
"At the end of the day, the future of this area is in the hands of its people"
Sami al-Nisf, Kuwaiti newspaper columnist
He said the resurgent Democrats might succeed in pressing Bush into a formula for withdrawing from Iraq.
However, Mustafa Alani, an Iraqi analyst for the Gulf Research Centre in Dubai, said: "The problem for Arabs now is that an American withdrawal could be a security disaster for the entire region."
He urged the Democrats to "think strategically as well as politically".
Sami al-Nisf, a columnist for Kuwait's Al-Anba newspaper, said the Democrat gains meant that there would be "no more rubber-stamping" of Bush's policies.
"But at the end of the day, the future of this area is in the hands of its people," he said.