Michael Dukakis and George Bush are courting Jewish voters in their race for the White House with pledges of continued support for Israel, but the Democrat is taking the Republican to task for recent U.S. policy in the Middle East.

Specifically, Dukakis is critical of Bush's stand on the sale of advanced arms to Arab nations, and the Massachusetts governor wasted no time chasing down the vice president before the 1988 B'nai B'rith International Convention.Speaking 2 1/2 hours later than Bush to the Jewish service group in Baltimore, Dukakis attempted to outgun him late Wednesday after Bush won a warm reception for his defense views from the American Legion convention in Louisville, Ky., despite an embarrassing confusion about the anniversary of Pearl Harbor.

Dukakis flew to Louisville to address the Legionnaires Thursday, although it was expected that Bush, on his way to East Texas to watch destruction of missiles under the Intermediate Nuclear Forces Treaty, would come out on top with the military group just as the Democrat emerged in better shape with B'nai B'rith.

Bush got a polite, friendly reception from the Jewish organization, but his rival's stronger, more pointed and personal speech - Dukakis's wife, Kitty, who joined him, is Jewish - drew more applause and more enthusiasm.

"The Republicans have sold AWACS planes to Saudi Arabia, Mavericks to Kuwait, Stingers to Bahrain and billions of additional dollars worth of sophisticated arms to Arab countries that refuse to make peace with Israel," Dukakis said, rattling off a list of weapons systems.

"George Bush has supported those sales and Dan Quayle has voted for them," he continued, referring to the Indiana senator Bush chose for his running mate.

"Lloyd Bentsen and I," he concluded, "are going to say no to Arab shopping lists that endanger the security of Israel."

Dukakis was cheered when he said the GOP ticket "doesn't acknowledge Israel's sovereignty over its capital, an undivided Jerusalem," which "we (Democrats) do." He also got in a dig at President Reagan by assuring the estimated 1,200 delegates that if elected, "there will be no trips to Bitburg" - the German cemetery Reagan toured amid outcries because of Nazi SS troopers buried there.

Bush's speech to B'nai B'rith never mentioned Dukakis by name and generally was an upbeat reaffirmation of his commitment to Israel's security, with a promise that "the American-Israeli strategic partnership is going to be even stronger" under his leadership than it is today.

"No wedge will be driven between us," Bush vowed, clearly vying for votes with Dukakis by appealing to support for the Jewish state.