The State Department and outgoing U.N. Ambassador Andrew Young remained at odds yesterday over whether Young will have further contacts with the Palestine Liberation Organization's representative to the United Nations during Young's final days in office.

Young said at a U.N. press conference yesterday that he may have to have discussions with the PLO representative in Young's role as the incoming president of the U.N. Security Council during next week's debate on the Palestinian issue.

Young's statement prompted a quick response from State Department spokesman Tom Reston, who said the administration does not anticipate that Young will have any further dealings with the PLO before he officially leaves his U.N. post, probably sometime next month. Reston said Young had been informed of the administration's position.

Young resigned as U.S. ambassador to the United Nations Wednesday after the disclosure that he had met with a PLO official in violation of U.S. policy and then misled the State Department about the meeting.

Young's resignation was a subject of debate and concern yesterday in political circles across the country and around the world.

A number of prominent black leaders criticized President Carter for having permitted Young to resign under fire.

Some Democratic Party officials predicted that blacks will not turn in anger against Carter at the polls in 1980 if Young keeps his promise and campaigns actively for the president's reelection.

And from overseas, Arab officials said Young's departure underscored their arguments that U.S. peacemaking efforts in the Middle East are biased toward Israel. The PLO praised Young as courageous and issued a particularly bitter denunciation of U.S. policy.

African states and black nationalist guerrilla groups generally lamented Young's resignation, with white minorities in southern Africa taking the opposite view.

The controversy over the resignation was fueled by Young at his news conference in New York City.

Young is expected to serve until a replacement is confirmed by the Senate which means he will be serving as president of the Security Council later this month, when the controversial issue of Palestian statehood is debated.

Yesterday, Young suggested that he would be willing to consult with anyone, including a representative of the PLO.

Noting that he would be serving as president of the Security Council, Young said, " . . . Anybody who wants to come there to consult can call the (U.N.) secretarial and get an appointment and I'll be there."

He said that if the PLO's observer at the United Nations, Zehdi Labib Terzi, requested an appointment, "it would be unconscionable to turn him down."

But State Department spokesman Reston issued a statement late in the day saying that, as president of the Security Countil, Young "is expected to meet with all member states of the United Nations who have business with the Security Council in accordance with traditional practice."

The PLO is not a member state of the United Nations, but participates as an observer.

Thus the administration statement made it clear that Young was expected not to meet with the PLO representative.

"When Ambassador Young presides over the debate, he will, in appropriate instances, afford the PLO an opportunity to speak in accordance with established practice," the statement continued, "We would not anticipate the need for him as Security Council president to have other dealings with the PLO.

"In his capacity as U.N. representative, he will pursue United States policy regarding contacts with the PLO," the statement said.

The presidency of the Security Council rotates among its member nations, with the United States serving in that post once every 15 months. U.S. representatives have never met with a PLO official while serving as Security Council president, Reston said.

In his news conference, Young blamed Israel for having first made public the fact that he met last month with the PLO's observer at the United Nations in violation of U.S. policy.

And Young said that the Israelis publicized the meeting despite his warning that such a disclosure would only create a new pro-Palestinian constituency among black-Americans.

Young said that, after learning of Israeli concern about the meeting, he had warned the Israeli ambassador to the United Nations, Yehuda Blum, that disclosure of the meeting would not be in Israel's interests.

"I said, in fact, that a big uproar over this issue only creates a constituency on the Palestinian issue that does not exist," Young said. "It was the Israeli government that decided to make this a public issue."

Young said that poor blacks suffer greatly from the high price of oil and that black leaders have a natural interest in a Mideast pease. He said that such vested interests had not previously been seen being an anti-Jewish interest. But now, Young addes, these interests "may be pro-Palestinian . . . in which case, the Jewish community will have a responsibility of finding a way to relate to that without being anti-black."

Word of Young's July meeting with the PLO observer first appeared in Newsweek magazine. A spokesman for Young, Thomas E. Offenburger, said that a Newsweek representative had told him the information originated from sources in Israel.

On Wednesday night, Young placed a conference call to six black mayors, including Washington's Marion Barry, to tell them the resignation was his idea, not President Carter's.

He urged them to work to soothe any anger his resignation may have among blacks and to tell them he hoped his resignation would not become a wedge between American blacks and Jews.

Yesterday morning, Carter telephoned Young to thank him for his remarks and his pledge to work for Carter's reelection, according to White House press secretary Jody Powell. Carter also thanked Young for having conducted himself "like a gentleman" throughout the ordeal, Powell said.

Yesterday, in his front public comment on the resignation, Carter told a group of community leaders from three states that Young had "decided on his own to resign" and "I accepted it with reluctance."

Last night Young met at a Washington hotel with officials of the Carter reelection committee and with Hamilton Jordan, the White House chief of staff.

A spokesman for the committee said the topic of the closed-door meeting, which had been scheduled a month ago, was how the Carter campaign can attract black support in 1980.

Others attending included Detroit Mayor Coleman Young, Carter campaign officials Tim Kraft and Evan Dobelle, and Jesse Hill, an Atlanta insurance executive.

White House officials say they hope that Young will be able to dampen the unrest among black leaders provoked by his resignation under fire. "As Andy gets around to black leaders and tells why he is committed to the president's reelection, hopefully that will ameliorate the present situation," said one Carter senior assistant.

A White House aide said Carter will not nominate a successor to Young until after the president's vacation, which begins today. While the selection process is just beginning, an informed source said, those in the running include Ambassador Donald F. McHenry, deputy U.S. representative to the United Nations, former member of Congress Barbara Jordan and former senator Dick Clark, the State Department specialist on refugees and an expert on Africa.