President Carter held the first of two days of scheduled meetings with Canadian Prime Minister Pierre Elliott Trudeau at the White House yesterday.

The meeting between the two lasted 80 minutes and was described as "cordial and friendly" in a statement issued by the White House. According to the statement, Carter and Trudeau discussed preparations for the international economic summit expected in late spring or early summer, the dialogue between developed and underdeveloped nations, arms sales, nuclear nonproliferation, the strategic arms limitations talks, reduction of troop levels in Europe and human rights.

Trudeau was the second neighboring head of state to travel here for talks with Carter since he took office a month ago. Mexican President Jose Lopez Portillo came last week.

Trudeau will address a joint session of Congress today. He was guest of honor at a White House state dinner last night.

Before Trudeau's arrival Carter met with his Cabinet. He also formally asked Congress to drop 19 dam-building and other "water resource" projects from the fiscal 1978 budget, saying they "appear unsupportable on economic, environmental and/or safety grounds."

Carter earlier announced his intention to recommend budget cuts for 18 projects, but yesterday he proposed that a 19th -- a massive reservoir in his home state -- be added.

"My God, that's hard for me to believe," said former Georgia Supreme Court Justice Peyton Hawes, who had pushed hard for the construction of the $231 million Richard B. Russell project on the Savannah River on the Georgia South Carolina border. "I know Jimmy pretty well and I got word from the White House last week that we didn't have anything to worry about," Hawes said in Elberton, Ga.

The President said he also has ordered a study, to be completed by April 15, of 301 other "current" federal water projects. He suggested that some of these, which were approved in times of lower interest rates, may no longer be cost-effective.

In other developments:

The President announced he will nominate Washington lawyer R. James Woolsey to be under secretary of the Navy. Woolsey, now with the law firm of Shea & Gardner, was general counsel to the Senate Armed Services Committee from 1970 through 1973.

Woolsey's wife, Suzanne Haley Woolsey, former policy analyst at the Department of Health, Education and Welfare and a member of the staff of the Urban Institute here, was named associate director of the Office of Management and Budget for human and community development. OMB Director Bert Lance also named four other principal assistants: W. Bowman Cutter, a former assistant to the president of the Washington Post Co.; Harrison Wellford, who was an aide to the late Sen. Philip A. Hart; Dennis O. Green, former Detroit finance director, and Hubert L. Harris Jr., former Atlanta bank executive.

Press secretary Jody Powell said Carter might hold a news conference this week and a Powell assistant said Carter told the Cabinet he may take defense and foreign affairs as the topic for a second "fireside chat" sometime in the next month or so.

A White House press spokesman said last night that the President and Vice President Mondale will meet with exiled Soviet author Vladimir Bukovsky early next week.

Powell's assistant, Rex Granum, said topics discussed at the Cabinet meeting ranged from the drought in the West to the bureaucratic paperwork burden to school desegregation.