The long-expected resignation of Jay Solomon as head of the General Services Administration was submitted yesterday to President Carter, who said he accepted it "with regret."

Solomon met with Carter yesterday morning, atter which White House officials made public the letter of resignation, which is effective March 31.

Sources said the president told Solomon he has not yet selected a successor. However, White House press secretary Jody Powell, suggesting that the selection process is almost complete, said a new GSA head will be named by the end of the month, and possibly this week.

In a letter to Solomon accepting his resignation as administrator of the scandal-ridden agency, Carter said:

"Because of your leadership and integrity, decades of waste and corruption at the GSA are now being exposed, and those who have betrayed the public trust are being identified and punished. That process will be continued and expanded."

The president added that Solomon's willingness to assist his successor after March 31 "will help us to insure that the investigations, reorganization and administrative improvements you began will be pursued aggressively."

In his letter to Carter, Solomon said he was resigning "in accordance with understandings reached in previous conversations."

This was a reference to earlier efforts by White House officials to ease Solomon out of his post at GSA.

Presidential aides have emphasized that Solomon has aggressively directed the investigation of corruption in GSA and is in no way tainted by the seandal. Moreover, Solomon, a wealthy Tennessee developer before he joined the government, has insisted that he always intended to resign at about this time.

Nevertheless, reports surfaced in January of White House unhappiness with Solomon and of a quiet search by senior Carter aides to find a replacement for him at GSA.

Some White House aides were upset by Solomon's willingness to discuss the GSA investigation with reporters, believing he was too anxious to claim credit for cleaning up the agency. White House aides hope to make administration efforts to end corruption a major element of the president's reelection campaign and are anxious for the credit for such achievements to go to Carter, not his appointees.

There also has been friction between Solomon and the White House since last summer over the manner in which Robert T. Griffin, a close friend of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), was fired as deputy administrator of GSA. To placate the angry speaker, the president later named Griffin to a high-salaried post in the office of the special representative for trade.

Powell said yesterday that Griffin was not among those being considered to replace Solomon.