Almost a third of the Jewish Americans questioned and almost half of the Arab Americans rated Mr Bush's performance as poor, in the survey conducted by the Arab American Institute (AAI) and Americans for Peace Now (APN).
Respondents from both communities indicated they supported a two-state solution including Palestine and felt the US should take a middle course in its approach to the conflict.
"The AAI/APN joint survey reveals that our communities are much more moderate on Middle East-related issues than people are often led to believe," said Debra DeLee, from Americans for Peace Now.
"Our poll also sends a message to decision-makers in Washington that Arab Americans and Jewish Americans at large want to see the US follow policies that will encourage the Israeli-Palestinian peace process, rather than detract from it," she said.
Pro-Israeli
Mr Bush's performance was rated "poor" by 31.3% of Jewish Americans and 46.4% of Arab Americans questioned.
Only 28.5% of Jews and 26.4% of Arabs rated his strategy "good" or "excellent".
Over 45% of Jewish Americans and more than 65% of Arab Americans said they thought the Bush administration should steer a middle course in pursuing peace.
But the largest proportion of respondents in each group said the administration's efforts at present were pro-Israeli.
Pessimism
The survey highlighted a high level of distrust between the two communities, despite a surprising amount of agreement on a number of issues.
The vast majority of respondents from both groups said they believed both Israelis and Palestinians had the right to live in secure and independent states of their own.
But most Arab Americans said they thought only around 50% of Jewish Americans thought Palestinians had a right to their own state.
And only around 40% of Jews believed Arab Americans thought Israelis had a right to their own state.
More than 40% of both communities said both sides shared the blame for the breakdown of the peace process.
But 41.3% of American Jews blamed the Palestinians and 31.2% of Arab Americans blamed the Israelis.
The two communities showed little sign of hope for the future.
Some 74.3% of Jewish Israelis and 58.9% of Arab Israelis were pessimistic about Middle East peace.
The AAI/APN survey conducted by Zogby International questioned 500 people from each community in late October 2002. The margin of error was 4.5%.