Democratic presidential candidate Michael Dukakis has closed the gap on Vice President George Bush in Utah, a new Deseret News/KSL-TV poll shows.

Bush, who will be the Republican nominee, still leads Dukakis 47-38, found pollster Dan Jones & Associates. But Dukakis, expected to be nominated at July's Democratic National Convention, has gained four points on Bush in Utah - by all accounts the most Republican state in the nation - since April.Two months ago, Jones found that 51 percent of those questioned favored Bush, 36 percent Dukakis.

In the latest poll, conducted May 31-June 1, 30 percent said they definitely would vote for Bush, 17 percent would probably vote for him, 23 percent would definitely vote for Dukakis, 15 percent would probably vote Dukakis, 3 percent would vote for someone else and 13 percent didn't know.

When Bush was matched against the Rev. Jesse Jackson, who will finish second to Dukakis in the Democratic race, he did much better: 73 percent for Bush, 16 percent Jackson, 5 percent someone else and 7 percent don't know.

Bush hopes that President Ronald Reagan's popularity in western states will help him carry the West this year. Jones found that Reagan is still highly thought of by Utahns.

Sixty-nine percent approve of the job the president is doing, 29 percent disapprove and 1 percent didn't know, Jones found.

Reagan's job approval rating slipped from the 80-percent level in Utah following the Iran/contra scandal, but still hovers around 70 percent, an excellent rating.

Bush didn't endear himself to Utahns by passing up an appearance at the U.S. Conference of Mayors meeting held in Salt Lake this week.

However, state GOP leaders say Bush will make a campaign visit to Utah sometime before the Nov. 8 election.

Both Dukakis and Jackson appeared before the conference and met with leaders of The Church of Jesus Christ of Latter-day Saints.

If the election for U.S. president were held today and the candidates were George Bush, Republican, and Michael Dukakis, Democrat, for whom would you vote?

Definitely Bush 30 percent

Probably Bush 17 percent

Probably Dukakis 15 percent

Definitely Dukakis 23 percent

Other 3 percent

Don't know 13 percent

If the election for U.S. president were held today and the candidates were George Bush, Republican, and Jesse Jackson, Democrat, for whom would you vote?

Definitely Bush 49 percent

Probably Bush 24 percent

Probably Jackson 7 percent

Definitely Jackson 9 percent

Other 5 percent

Don't know 7 percent

How would you evaluate the job performance of President Ronald Reagan?

Strongly approve 30 percent

Somewhat approve 39 percent

Somewhat disapprove 17 percent

Strongly disapprove 12 percent

Don't know 1 percent

Sample size: 607; margin of error plus or minus 4 percent