Bush on Monday said he backed Israel's right to "self-defence". His remarks came after an Israeli air raid the day before on an alleged training camp for Palestinian fighters in Syria.
The Israeli raid followed a Palestinian bombing that killed 19 people in Israel on Saturday.
The US president's comments will concern Arab governments and other critics of Israel, as they appear to endorse actions such as Sunday's airstrike in Syria. The Israeli attack was widely condemned by the international community except in the US.
Bush said he had told Israeli Prime Minister Ariel Sharon on Sunday that Israel should not feel constrained in defending itself.
"However, I said that it's very important that any action Israel take [sic] should avoid escalation and creating higher tensions," Bush said in Washington.
White House spokesman Scott McClellan said the United States had urged both Israel and Syria to avoid "actions that heighten tensions or that could lead to hostilities".
But tensions continued to rise throughout Monday. The Israeli army said one of its soldiers had been shot dead at Israel's border with Lebanon, and military sources blamed his death on Hizb Allah guerrillas backed by Iran and Syria.
Hizb Allah denied its forces had been involved in any shooting.