President Carter lashed back at Ronald Reagan's criticism of his energy policy yesterday, and named John Sawhill chairman of the new Synthetic Fuels Corp.

The president, who picked up a string of personally delivered endorsements earlier in the day, replied to Reagan's charge that his administration has discouraged energy exploration and production.

"Gov. Reagan is wrong. He's again made an accusation without checking the facts. Let me tell you the truth," Carter said.

Coal production will set a single-year record and crude oil production increased this year for only the second time in a decade, Carter said. U.S. oil production is now 8.6 million barrels a day.

It was the second straight day that Carter was quick to respond to Reagan. "I do not intend to let my Republican opponent continue to misrepresent the facts about this administration . . .," the president said.

Carter said his selection of Sawhill, now deputy secretary of energy, followed a search of several weeks. Sawhill held energy posts in the Nixon and Ford administrations, and he was later president of New York University.

The organization he will head, formerly called the Energy Security Corp., aims to encourage American production of two million barrels per day of synthetic fuels by 1992. It will be funded by $20 billion from the tax that Carter proposed and Congress levied last year on crude oil; and will provide loan guarantees and other financial support to development of synthetic fuels.

The president also has chosen the six board members of the corporation. Their names are to be made public today.

White House press secretary Jody Powell pointed out that Reagan has consistently opposed the tax on energy companies' increased profits flowing from the Carter administration's decision to deregulate oil prices.

Carter called the corporation "a cornerstone of the national energy policy."

"It's our main instrument in cutting the intolerable overdependence of our nation on imported oil," he said.

The president received visits and endorsements from the Democratic members of the New York congressional delegation, a group of 22 environmentalists and New York financier Felix Rohatyn.

Rohatyn, who advised John B. Anderson earlier in the campaign, and the others emerged from their meetings with the president to warn that Anderson stands no chance of winning the election and a vote for him only aids Reagan.

"The possibility of the Anderson campaign siphoning support from the president and throwing our 41 electoral votes to Gov. Reagan is one which must be avoided," Rep. Samuel S. Stratton said as chairman of the New York congressional delegation.

Stratton referred to the state Liberal Party's endorsement of Anderson as a threat. "The welfare of our state would be severely jeopardized with a Democratic defeat," he said.

Rohatyn, who was instrumental in arranging programs that rescued New York City from bankruptcy, said he knows New York will need more federal assistance and he would rather ask a Carter administration for help than a Reagan administration.

Rohatyn is chairman of the Municipal Assistance Corp. formed to help New York City untangle its financial disaster.He contributed to Anderson's campaign and helped the then-Republican, now-independent candidate organize a meeting with business leaders.

Carter campaign chairman Robert Strauss escorted Rohatyn from the White House to meet reporters on the lawn.

The environmentalists, who receded Rohatyn before the cameras on the lawn, represent most of the leading environmental organizations in the nation, but they endorsed the president as individuals.

Russell Peterson, a Republican who worked in the Nixon and Ford administrations, said: "I'm increasingly fearful of what the election of Ronald Reagan will mean to my children and grandchildren."

Rafe Pomerance, president of Friends of the Earth, said Anderson's environmental record in the House "is mediocre at best." He ranked in the lower half of House members on environmental matters, Pomerance said.