President Reagan welcomed Secretary of State Alexander M. Haig Jr. home yesterday from the NATO foreign ministers' meeting in Rome with a public pat on the back apparently aimed at ending speculation about continued friction with White House aides.

"He comes home in triumph," Reagan said, in one of the few appearances he has made before reporters and cameramen since returning to the White House following the March 30 attempt on his life.

"It was a most successful meeting in a situation that could have been critical for us in regard to our allies," the president said with Haig standing beside him. The two men stepped from the White House onto a covered walkway to have their photographs taken and make brief remarks to reporters. They declined to answer questions.

Haig has been criticized by White House aides for not being a team player in an administration that places great importance on consultation and teamwork. The secretary quickly established a reputation for a quick temper and abrasive manner. He reportedly threatened to resign half a dozen times during various disputes in the first two months of the administration.

Public disputes with senior White House staff members ove the handling of foreign policy and the management of crises gave rise to speculation that Haig would prove unable to fit into the Reagan administration for the long term, but since late March the president's top aides have sought to counter such talk with assurances that the problems were behind them.

Reagan's effusive praise of Haig yesterday gave his personal stamp of approval to the way the secretary has been performing his duties.

"It is a triumphal return," Reagan said of Haig, who arrived here early yesterday. "I think we have a better relationship with our allies now that we saw many points of difference that might have existed there, and some [allies] erased their worries about our relationship with the Soviet Union."

The North Atlantic Treaty Organization's 15 foreign ministers agreed to a communique that followed Reagan administration policy by linking improvement of East-West relations to Soviet international behavior.

At the same time, the United States took a step its allies pressed for, expressing willingness to explore talks with the Soviets on limiting intermediate-range nuclear missiles based in Europe.

Neither the president nor White House spokesman Larry Speakes explained exactly what Reagan had in mind when he said the NATO session could have been critical for U.S. relations with its allies.

Haig quoted NATO Secretary General Joseph Luns as describing the meeting as "perhaps the most important that has occurred in recent years."

In brief remarks following Reagan's, the secretary of state said the Rome meeting underlined solidarity with Washington's European allies, which he called "the most important objective of American foreign policy." He added that Reagan's foreign policy received "unanimous, enthusiastic endorsement" from all NATO members, "a major achievement, of which we're all very proud."

Their remarks concluded, Reagan and Haig returned to the Oval Office for further briefings on the NATO talks and the visit, beginner today, of Japanese Prime Minister Zenko Suzuki.

In other developments, Reagan named three inspectors general: Joseph A. Sickon for the General Services Adminitration, K. William O'Connor for the Community Services Administration and John V. Graziano for the Department of Agriculture.

He also named John S. Herrington to be deputy assistant to the president for personnel and Jose S. Sorzano to be the U.S. representative on the U.N. Economic and Social Council.