In an interview published on Wednesday he also said some in Washington might want war with Syria.
The comments to Spanish newspaper El Pais and Italy's La Repubblica were published a day after US President George Bush imposed economic sanctions on Syria and accused Damascus of supporting terrorism.
"For the first time the United States has turned into a source of instability instead of stability ... The war in Iraq has unleashed a hatred that is finding an echo in terrorism," al-Asad said.
The Syrian president said the United States should instead help combat terrorism in its neighbour Iraq and in the Palestinian territories by adopting a "fair" political position, and by fostering economic development and cultural understanding.
Al-Asad said that Syrian-US relations were complicated by conflicting messages from Washington.
"There is one current that wants to cooperate with Syria through dialogue and reciprocity, and another that does not want this contact and is looking for pressure and perhaps war," al-Asad said.
George Bush says Syria is letting
anti-US fighters to enter Iraq
Syria had suffered from the US occupation of Iraq, al-Asad said, citing a fall in foreign investment in the region and heightened tensions between Syria's own tribes and families.
"Now we are going to see the effects on security. Iraq is chaotic and uncontrolled, there are arms being smuggled out toward Syria, also a rise in extremism and a feeling of hatred toward the United States which did not exist before."
In ordering sanctions on Tuesday, Bush accused Damascus of supporting terrorism, pursuing weapons of mass destruction and failing to prevent anti-US guerrillas entering Iraq.
The sanctions ban US exports to Syria except for food and medicine, freeze assets of Syrians the United States suspects of terrorism, and prohibit Syrian flights to and from the United States.
But al-Asad said democratic and economic changes within Syria were moving slowly because security had taken priority.
"The economic situation is going backwards," he said, but added that Syria had made progress in starting private banks, universities and newspapers. Private broadcasters were next, he said.
Meanwhile, the head of the Arab League said on Wednesday that US sanctions on Syria were inspired by Israel and would further hurt US-Arab ties.
"In whose interests is this (the sanctions)? Is it in the interests of Arab-American relations? Definitely not. Is it in the interests of stability in the Arab region? Definitely not," Arab League Secretary General Amr Musa told reporters.
However, the Israeli government strongly supported the sanctions.