President Reagan has surged into a 19-point lead over prospective Democratic presidential nominee Walter F. Mondale, according to a Gallup Poll released today.

The survey of 908 registered voters, taken June 22-25, gave Reagan 56 percent and Mondale 37 percent, with 7 percent undecided or supporting other candidates. The theoretical sampling error is plus or minus 4 points.

Reagan led Sen. Gary Hart (D-Colo.) in a separate trial heat by 12 points, 53 to 41 percent, with 6 percent undecided.

Reagan's current lead is the largest an incumbent president has enjoyed at this stage of the race since 1964, the year of President Lyndon B. Johnson's landslide victory over Sen. Barry Goldwater (R-Ariz.). At a similar point in 1972, President Richard M. Nixon had a 16-point lead over Sen. George McGovern (D-S.D.), who carried only Massachusetts and the District of Columbia in November.

On the other hand, President Gerald R. Ford trailed challenger Jimmy Carter by 18 points in the June, 1976, Gallup Poll and came back to make it a close race. At this time four years ago, Reagan led President Carter by 7 points.

The breakdown of the most recent Gallup Poll showed Reagan ahead of Mondale among men and women, in all age categories, and in all regions. Mondale led in only three of Gallup's standard categories: among self-identified Democrats, blacks and people with less than high-school educations.

Mondale's showing in the trial heat was his weakest this year and indicated that the customary consolidation of support after the last primaries has not occurred. In January, the year's first Gallup Poll showed Mondale trailing Reagan by 1 point, and as recently as early May his deficit was only 4 points.

The latest Gallup Poll is consistent with the Reagan campaign's claim that its national poll taken after the final round of Democratic primaries on June 5 had Reagan 16 points in front.

James Lake, a spokesman for the Reagan reelection committee, said he believed that the widened margin resulted from "two months of very positive news for the president, both on his foreign trips and in the domestic economy . . . along with the fact there's just no great enthusiasm among Democrats for Mondale. Now that the realization has set in that he's their nominee, we're picking up support from Democrats who see no hope in his leadership."

James A. Johnson, Mondale's campaign chairman, said he found the poll results "totally implausible" and said they were at odds with other data he had seen. "The polls will move up and down," Johnson said, "but we're confident Mondale will run a strong race."

Kathy Bushkin, Hart's press secretary, said the poll provided ammunition for Hart's continuing effort to convince Democratic delegates that he would be a stronger candidate.

Since May 3-5, when both Mondale and Hart trailed Reagan by 4 points, their strength has increasingly diverged. In successive May and June polls, Mondale trailed Reagan by 10, 9 and 19 points, while Hart's deficit went from 7 to 11 to 12 points. Bushkin commented, "It's not that great a margin but it's a margin that can make a difference" in an election.

The breakouts of the basic numbers are encouraging to Reagan. There is still a significant "gender gap," but Reagan leads Mondale by 8 points among women and by 30 points among men.

The oldest president to seek reelection, Reagan shows his greatest strength among young voters. He has a 10-point lead over Mondale among over-50s, a 22-point lead among those between 30 and 49 and a 33-point lead among those under 30. He leads in all sections of the country, with a 13-point lead in the East, a 19-point lead in the Midwest, a 21-point lead in the South and a 23-point lead in the West.

Reagan is winning 61 percent of the white votes, while Mondale takes 72 percent of the black votes. Mondale gets 8 percent of the Republicans; Reagan takes 24 percent of the Democrats and leads 66 to 24 percent among independents.

The general pattern of support for Hart is similar to that of Mondale, but there are several voter groups where they have significantly different levels of support. Hart runs 12 points ahead of Mondale among voters under 30, 12 points better in the West, and 10 points better among independents. Mondale, on the other hand, runs 10 points better among blacks.