President Reagan, home from the economic summit in Venice, is preparing for a new round of combat with the Democratic-controlled Congress over the budget, trade and other domestic policy priorities.

Reagan will play his opening hand in a nationally televised address from the Oval Office Monday night in which White House officials say he intends to challenge Congress to overhaul the budget process.

The president may also suggest to Congress the adoption of a set of economic principles that would preserve his priorities after he leaves office in 20 months.

One senior official said Monday's address will try to "get the debate focused on our domestic economic policies and get Congress to face facts -- to put in place a budget process that is reliable and credible."

Reagan is also facing a series of potential veto confrontations with Congress over a money bill containing arms-control restrictions he opposes, a trade bill that he has labeled protectionist, and a housing bill that exceeds his budget request.

The senior official foresees many potential conflicts between now and the August congressional recess. Reagan is planning to visit Capitol Hill this week to lobby on the trade bill that is expected to reach the Senate floor shortly, and he used his weekly radio address yesterday to speak out against restrictive trade provisions.

Also this summer, Reagan is expected to try to build support for a prospective treaty to eliminate medium- and short-range missiles from Europe. Reagan said Friday in Bonn that he expects Soviet leader Mikhail Gorbachev to come to the United States this year to sign such a treaty, which would require Senate ratification. Reagan is expected to announce in the Monday address that he has ordered an affirmative response to the Soviets on the "double-zero" plan for eliminating missiles in Europe, with some conditions attached to satisfy the allies.

White House officials also say they expect to spend part of the summer grappling with the Iran-contra hearings. Since the hearings began in May, Reagan has attempted to advance his policy agenda without regard to the controversy, but the televised proceedings remain a source of attention and concern to his advisers.

Last week at his Venice news conference, Reagan spent about as much time answering questions about Iran-contra as about the summit and the Persian Gulf. White House officials have been angry at Secretary of State George P. Shultz for his vigorous defense of Assistant Secretary Elliot Abrams after he admitted misleading Congress.

On budget priorities, the president and the congressional Democrats have been at odds all year, with Reagan continuing to oppose tax increases or defense cuts. White House strategists have watched with satisfaction as the Democrats argue among themselves about alternatives to Reagan's priorities. During this period, Reagan spurned Democratic appeals for a summit or negotiations on the budget.

As White House officials view it, the next phase is for Reagan to launch a public campaign for his own budget priorities and for some kind of overhaul of the budget process. Reagan intends to make a series of appearances around the nation in the next few weeks to highlight this theme.

The White House has yet to embrace a specific plan for overhauling the budget process, but Chief of Staff Howard H. Baker Jr. has had extensive talks with congressional leaders. White House officials say an agreement on changing the process could pave the way for a compromise on the budget itself.

However, there are few signs that Reagan is willing to offer any concessions, such as increased taxes or defense cuts. Some White House officials said he is so intransigent on these points that he would rather leave office next year defending his priorities than make progress against the deficit by compromising.

Despite Reagan's assertion that the United States reduced the deficit by $40 billion last year, allied leaders in Venice complained to him that the U.S. fiscal imbalance was also hindering their economies.

The push for an overhaul of the budget process stems in part from the deadlock that has developed between Reagan and Congress over defense, tax and domestic spending priorities in recent years, resulting in a huge catchall spending bill at fiscal year's end.

Budget revision is also motivated by Reagan's repeated complaint that Congress failed to cut domestic spending as much as promised after the big 1982 tax increase. While this is disputed by congressional analysts, aides say Reagan has accepted it as fact and he is unwilling to negotiate with the Hill unless given assurances that the deal is enforceable.