President Carter embarking on his first venture overseas since taking office, arrived here tonight with warm words about the "historic ties" that bind the United States and Britain.

Coatless and carrying a small briefcase under his arm, Carter stepped off Air Force One into a light rain and onto a red carpet at Heathrow Airport.

He was welcomed by British Primie Minister James Callaghan "on behalf of this whole continent of Europe, which has always been closely linked with the United States."

The President's arrival here marked the beginning of five days of meetings that will bring him in personal contact with the leaders of the most important American allies and several other European political and government figures.

The main purpose of Carter's trip is a two-day summit conference on economics and related issues to be held here Saturday and Sunday. The other participants will be Callaghan and the leaders of West Germany, France, Italy, Canada, Japan and the European Economic Community.

Carter is to fly Monday to Geneva for a meeting and "working dinner" with Syrian President Hafez Assad, and attend a meeting of the North Atlantic Treaty Organization here Tuesday before returning to the United States that night.

In addition, White House officials announced today that while in Europe the President will meet with several other officials, including Prime Minister Constantine Karamanlis of Greece, Prime Minister Suleiman Demirel of Turkey and Callaghan's political opposition British Conservative Party leader Margaret Thatcher.

Early in his administration, Carter sought to take initiatives toward solving Greeks-Turkish differences over Cyprus. His meeting with Thatcher is likely to be a courtesy call, designed to balance somewhat what is certain to be a highly publicized tour of north-eastern England that he will take with Callaghan on Friday.

Enroute here, the President was asked by reporters aboard Air Force One whether he would propose any economic initiatives at the summit. He replised that he would, but refused to elaborate.

In fact, neither Carter nor Calllaghan spoke in substantive terms at the airport, making the arrival in the rain and the glare of television lights strictly a ceremonial affair.

The President grinned broadly through Callaghan's welcoming remarks, in which the British Prime Minister said they were about to embark on "a great venture" having to do with "overcoming proverty, trying to put out people back to work and trying to get our economics in a healthier state."

Carter singled out Callaghan for praise, calling him "the leader of the European community."

Referring to his tour of northeastern England, which will take him to the ancestral home of George Washington, the President said this was "symbolic of the ties that have always bound us together."

The aides who are assisting Carter on his first presidential trip abroad included Secretary of State Cyrus R. Vance, Treasury Secretary W. Michael Blumenthal and National Security Adviser Zbigniew Brzezinski.

Carter personally ordered the size of the American contingent held down, but nonetheless brought along his son, Jeff, and his chief political adviser Hamilton Jordan in addition to the aides who normally travel with him.

The President has said this will be his only foreign trip this year. Discussing it with reporters on Air Force one, he said he was excited about it "in a way" and added:

"I don't have any deep yearnings for overseas trips. It would suit me fine if I stayed at home. But I think it is a worthy trip and I'm looking forward to it. I feel so crammed with information and advice that it reminds me of the presidential debates."

At the conclusion of Carter's remarks at the airport, Callaghan turned to him and said, "Very Good."

"Ah come on," the President replied.