Washington — The Democratic presidential campaign is entering a new phase. After months of disarray and bickering in the primaries, the Democrats have begun the deliberate process of healing the battle wounds and moving toward what they hope will be a smooth, harmonious national convention and a party united under the banner of Walter Mondale.
The get-together in New York Tuesday of the former vice-president and Gary Hart, his principal rival, is viewed as singularly important for party unity.
''I think we have a great prospect for a positive message going out from the convention rather than the squabbling about rules,'' says Michael R. Steed, national director of the Democratic National Committee.
Robert Strauss, former party chairman and a prime mover behind the scenes, stresses that Mr. Mondale has had the burden of being in a negative, contentious stance since the beginning of the year. With the Tuesday summit aimed at ending the acrimonious Mondale-Hart feud, Mr. Strauss told reporters at breakfast, ''This may be the . . . first day of the positive-postured campaign.''
After their two-hour fence-mending summit, Mondale and Senator Hart struck a pose of friendship and determination to present a united front in the face of a formidable Republican challenger. ''Walter Mondale and I are united by two common beliefs and objectives,'' said Hart, referring to ''the principles of our party'' and ''our profound fear of a second Reagan term.''
''Fritz and I have been friends, are friends, and will continue to be friends ,'' Hart added.
''We both agree that this is an election that must be won,'' commented Mondale. ''It is our shared objective.''
Amid all the public bonhomie, the Jackson factor remains a troublesome problem, party leaders say. The visit of Jesse Jackson to Cuba at the very time that nominee-apparent Mondale was sounding the theme of reconciliation is seen as damaging to the party's image.
''It's the worst possible thing we need - Jackson having breakfast with Fidel while Mondale and Hart are trying to make peace,'' says one Democrat.
But Democratic strategists say they are sanguine that the campaign is now moving into a more positive, forward-looking mode. Other recent developments are cited for their optimism:
* Mondale is looking carefully and judiciously for a vice-presidential running mate. An array of potential nominees have met with him at his Minnesota home, including Los Angeles Mayor Thomas Bradley, San Francisco Mayor Dianne Feinstein, and Texas Sen. Lloyd Bentsen. Mondale and Hart said they did not discuss the vice-presidency in their get-together, but Mondale told reporters he is considering Hart as well.
* Edward M. Kennedy has heartily backed the Mondale candidacy. The endorsement of the senator from Massachusetts, the last remaining power figure outside the primary contest and a strong Democratic symbol, is extremely important for party harmony.
* The Mondale-Hart summit came a day after the Colorado senator announced that he would not challenge several hundred Mondale delegates to the convention, thus ensuring Mondale's nomination.
''I will take no part in any action that makes our convention one of divisiveness or rancor,'' said Hart in a letter to the Democratic national chairman, Charles T. Manatt.
Of concern to Democratic leaders, however, is the stand Mr. Jackson will take at the convention next month. He has been pressing for a change in the party rules, pointing to the fact that he received a disproportionately small share of the delegates, given the popular vote he won in the primaries. But the party rules committee has adopted a set of rules that do not address the Jackson concern for better representation. The Jackson delegates on the committee voted against the rules.
Growing pressure to put a woman on the ticket is another ingredient in the still-bubbling Democratic political pot. Some political observers speculate that failure to select a woman now, after the dramatic emergence of the issue, might lead to contention at the convention. But Democratic planners maintain that ranks will close, whomever Mondale chooses.
''Most women make a point of saying that if Hart or someone else is the nominee, that would be understood,'' says Ann Lewis, political director of the Democratic National Committee.
To adopt a positive party tone is one thing, but to translate this into an effective challenge to Ronald Reagan is another, political observers say. Democratic strategists are acutely conscious that the Democratic nominee faces a President who remains high in the approval ratings and is widely perceived as a strong leader. Strauss spoke of him as ''good'' and ''decent'' man who must be taken on not for his character but for his performance and knowledge in dealing with the presidency - and even then gingerly.
''If you take on Ronald Reagan head-on, you're going to get the worst of it, '' he told reporters. ''You have to take him on sideways and in a more delicate way . . . taking him on head first, he'll destroy you. He's too good an actor.''
Strauss said it was ''amazing'' that Mondale was running only 15 points or so behind the President, given the fact that ''he has had six months or more without one absolute positive day in the press'' and Reagan ''has not touched a tough problem in months.'' This shows ''there are weaknesses out there that can be exploited.''
Once the public is ready for the issues to be joined - Central America, East-West relations, arms control, fairness, deficits - the Democrats will be able to pick away at the President's ratings, Strauss said. Moreover, he said, Mondale has proved he is a ''fighter'' and is a ''better general-election campaigner'' than generally thought.
But a major problem for Democrats will be money. Republicans, Strauss said, turn on money ''like water from a spigot'' and will have far more funds to spend on the campaign. Democrats, he admitted, have not done a good job of fund raising.