The U.S. Embassy said Saturday it will resume processing thousands of Soviets who were promised refugee status in the United States but were left stranded because of a lack of State Department funds.

The embassy also announced that it will ask prospective refugees, their relatives in the United States and private organizations to help pay the refugees' way to America.The U.S. government had been helping finance travel to and resettlement in the United States. The statement did not say what the refugees were being asked to pay. It said processing would resume Monday.

U.S. diplomats in Moscow say applications of about 3,400 people who were granted refugee status have been frozen since July 1, when the State Department decided to delay processing until Oct. 1, the start of the new U.S. fiscal year.

The department cited an increase in refugees and a shortage of funds.

Last month, the U.S. Embassy gave permission to a record 2,063 Soviets to immigrate to the United States. It expects to issue 9,500 visas for Soviet immigration to the United States in the 12 months ending Sept. 30, 1988.

The delay left hundreds of prospective emigrants stranded in Moscow after they sold their homes, quit their jobs and traveled to the capital expecting to be allowed to leave for the United States.

Saturday's announcement followed sharp criticism in Washington of the State Department decision.

On Friday, 23 senators sent a letter of protest to President Reagan.