Four Democratic presidential candidates pledged to improve the nation's schools at a session here today with Democratic governors, and tried to assure the state executives that they will prevent President Reagan from taking the education issue away from them in the 1984 elections.

The four of the six Democratic hopefuls who attended--former vice president Walter F. Mondale, Colorado Sen. Gary Hart, South Carolina Sen. Ernest F. Hollings, and former Florida governor Reubin Askew--outlined their programs to raise teacher salaries and meet other challenges outlined by various national commissions that have studied the declining quality of America's education system.

But in a question-and-answer session with the governors, whose session was a prelude to the National Governors Association meeting that officially begins Sunday, Utah Gov. Scott M. Matheson, noting the recent White House attention to education, asked, "Has Ronald Reagan taken away the issue from the Democrats, and if so, what can we do? How can we carry the day on the issue in 1984?"

Mondale, calling Reagan's the most anti-education administration in history, replied, "He is dealing with the politics of the problem, not the problem," as he tried to assure fellow Democrats that the president's recent initiatives have not overtaken what was described as a Democratic commitment to education that began with Thomas Jefferson.

Askew said he believed that Reagan, in elevating the issue, has "helped us."

The four Democrats differed in detail in their financial commitment to the schools, with Hollings, as before, the high bidder with a $14 billion plan that calls for $5,000 bonuses for all teachers in the country and $10,000 extra for those teaching in inner cities.

"The issue is not merit pay, the issue is base pay," said Hollings, who drew the best response from the audience with his attacks on Reagan and his southern aphorisms.

Hollings advocated elimination of the MX missile or the B1 bomber, two costly weapons systems favored by Reagan, and transferring some of the savings to improve the schools. "Certainly the children of America are worth at least one weapons system," he said.

Mondale, noting that much of the leadership on education reforms is coming from Democratic governors, restated his $11 billion program and called for an enlarged federal role to save schools from what the National Commission on Excellence in Education has called "a rising tide of mediocrity."

"If it's going to be solved, it's got to be done with presidential leadership," Mondale said.

Hart, saying that the American economy of the next century will depend not on machines but on brainpower, said he favors legislation patterned after the National Defense Education Act.

"We must link education very directly" to the nation's ability to compete in the world economy, Hart said, urging support for additional legislation tying education to emerging industries.

Askew was less specific in his dollar commitment, but made clear that he sees the presidency as a pulpit from which to bring together the elements of the country that could forge a consensus on how to improve the schools.

He also warned that, in the face of $200 billion annual deficits, the federal government may not be in a position to supply the states with considerably more money.

Askew said the federal role was "not of a great supplementer, but of providing incentives" to ensure quality schools.

The session was chaired by Virginia Gov. Charles S. Robb, who noted how important education had become as a political issue in the presidential campaign by reminding the governors and candidates that the subject was hardly a topic of discussion in 1980 and 1976.

Matheson added that public opinion polls in his state showed education to be the dominant issue for most voters and he predicted that it would be "the most important issue to come out of the next presidential election."