NEW YORK (AP) _ Jesse Jackson drew one in five white votes Tuesday in Connecticut's Democratic primary, far more than in 1984 but too few to deny Gov. Michael Dukakis a big win, exit polls said.

Jackson's white support, up from about 5 percent four years ago, was bolstered by a nearly unanimous black vote, WNBC-TV and ABC News polls said. WNBC said Jackson drew 18 percent of the white vote; ABC said 22 percent.

But WNBC reported only one-fifth of the Connecticut Democrats said the nation was ready to elect a black president, and ABC found that a third of Democrats said they would abandon the party and vote for George Bush if Jackson were nominated.

ABC poll analyst John Brennan noted that Jackson's share of the white vote was about the same in Massachusetts and Rhode Island and greater in Vermont early this month, before Jackson's victory Saturday in the Michigan caucuses.

''There's been a misconception that Jackson has made some kind of substantial breakthrough with the white vote,'' Brennan said. ''I don't think that's happened.''

Both the ABC and WNBC polls said Jackson's white backers were mostly liberal and well-educated, rather than blue-collar workers.

Dukakis, the governor of neighboring Massachusetts, won all demographic groups except blacks, and 60 percent of the Democrats, including a third of those who voted for Jackson, said they believe he will be the nominee.

But the NBC poll of 1,700 voters also found some weakness in Dukakis' support: 45 percent of those who voted for him said they wished there were other candidates running, said poll director Laurily Epstein.

''There's good news for him; he's swept all groups except blacks,'' she said in a telephone interview. ''But there's disquieting news in that it's not enthusiastic support.''

The ABC poll, however, found that 79 percent of the Democrats said they would vote for Dukakis if he were the nominee against Bush; only 52 percent of Democrats said they would vote for Jackson if he were nominated, and 33 percent said the nomination of Jackson would cause them to back the Republican.

NBC said there was a hint of trouble for Bush: Forty percent of Republican voters did not think he has told the full story of the Iran-Contra affair, and they tended to support him less strongly, Epstein said.

''Among those for whom it's an issue, it's hurting him,'' an indication of a potential trouble spot in the general election, she said.

Still, Bush was viewed favorably by 75 percent of the Republican voters and unfavorably by 18 percent, the WNBC poll said. Dukakis had the best such rating among Democrats, 70 percent favorable to 10 percent unfavorable.

Jackson was viewed favorably by about half the Democratic voters and unfavorably by a third, while Gore was viewed favorably by 40 percent and unfavorably by a quarter. Only one in seven Gore supporters think he will be the party's nominee, WNBC said.

Jackson improved his showing among black Democrats as well as whites, winning 90 percent of the black vote compared to 69 percent in 1984, NBC said. Though just 20 percent of Democrats said the nation is ready to elect a black president, that was up from 10 percent in 1984.

ABC polled 1,277 voters in Connecticut; Brennan said the margin of sampling error was about 5 percentage points. WNBC's was about 3 points.