The Reagan administration's economic and trade policies could do great damage to U.S. relations with Western Europe, Italian Foreign Minister Emilio Colombo told Secretary of State George P. Shultz here yesterday.

Colombo, the first European foreign minister to meet with the new secretary of state, said he outlined to Shultz several complaints involving recent issues including administration trade sanctions against construction of a new natural gas pipeline from the Soviet Union to Europe and its ruling last month that seven Western European countries had illegally subsidized steel imports.

He also raised longstanding European complaints about high U.S. interest rates and unemployment, which many European leaders believe have been exacerbated by administration policies.

Colombo thus added his voice to those of other European officials who have warned that the United States and Western Europe face what may be the gravest crisis in their relations since the end of World War II.

Unless some administration policies are altered, Colombo warned, there would be "negative consequences both economically and politically and a deterioration of European relations with the United States."

Speaking to reporters after the hour-long meeting, Colombo said the sole beneficiary of such deterioration would be the Soviet Union. "It is essential to keep a united front," he said.

He called U.S. policies "fragmented . . . in our opinion there is no overall view" and noted the contrast between the administration's decision to lift the embargo on selling grain to the Soviets with its hard line on the pipeline, a decision that could cost private European suppliers as much as $750 million, according to U.S. estimates.

Colombo also criticized what he called the "unilateral" nature of the pipeline decision, which President Reagan has said was made in retaliation for the martial-law crackdown in Poland.

Colombo indicated he believes that the president's decision June 18 further tightening the restrictions was made without adequate consultation with European allies.

Colombo said Shultz expressed awareness of problems between the United States and Europe and promised "a new global assessment" of administration policies. The State Department had no comment on the meeting.

The administration's handling of relations with Western Europe also came under attack on Capitol Hill. Rep. Lee H. Hamilton (D-Ind.), chairman of the House subcommittee on Europe and the Middle East, criticized Reagan's statement at a news conference last month that problems with the European allies had been "largely eliminated."

Hamilton cited sharply contrasting statements by European leaders who have accused the United States of ignoring European interests, particularly in regard to policy on the Soviet Union.

"You get the impression that the leadership on both sides of the Atlantic are talking about two different relationships," he said.

Robert Hormats, assistant secretary of state for economic and business affairs and one of the witnesses appearing at a subcommittee hearing, conceded that "one has to acknowledge candidly there are tensions."

But Hormats said areas of common interest "far outweigh the differences between us. . . . The last thing we or the Europeans want to do is to demonstrate divisions between us which have the effect of weakening the NATO alliance."

In a related matter, Colombo said Italy is willing to participate in an international peace-keeping force in Lebanon if all parties in the dispute agree to such a force.