Premier Adolfo Suarez heads for the United States Wednesday on a three-day trip intended to bolster Spain's economic and political relations with the Carter administration.

The 44-year-old premier, "pointman" of King Juan Carlos' program to turn Spain into a democracy, is aware that a welcome by this country's principal ally will strengthen his position in the June 15 parliamentary elections and curb military opposition sparked by his Easter week decision to legalize the Communist Party.

The United States has given every indication that it approves the policies of the king and his premier whose performances are getting special attention, according to U.S. officials. But Spain is looking for more than sympathy.

In a scheduled two-hour meeting with President Carter, Suarez is sure to bring up serious differences between Madrid and Washington in nuclear power, diplomatic sources here say. Spain is reconsidering contracts for the construction of eight American nuclear reactors.

Saurez is to spend the first two days of his visit in New York, promoting Spain's new democratic image at the United Nations. He is to deliver Spain's ratification of the U.N. human-rights conventions and meet with Secretary General Kurt Waldheim to explain the advances his country has made toward democracy in the 17 months since the death of Generalissimo Francisco Franco.

He has also scheduled a session with Jordan's King Hussein, another visitor seeking to discover the attitudes of the new Democratic administration in Washington. Spain which does not recognize Israel, is vitally interested in the Middle East. Earlier this year the premier was forced to cancel plans to visit the region because of an outbreak of political violence in Spain.

In New York Saurez quill pursue one of the most important objectives o the trip - discussions with American banking and business leaders for a $1 billion loan to support the sagging Spanish economy in the transition to a democracy. He is to travel to Washington Thursday evening and stay at Blair House.

Spanish officials described the trip as aimed at "consolidating" Spain's imaged as a budding democracy. King Jaun Carlos, officials said, promised during his U.S. visit last summer to establish a democracy.

The premier, officials say, intends to underline that he has accomplished what the king pledged and, at the same time, to ask the Carter administration and American bankers for political and economic help to cushion the change.