Egypt and Israel agreed yesterday that their deadlocked negotiations on Palestinian self-rule, which were broken off abruptly in mid-May, will resume Thursday in Cairo.

The announcement was made at a State Department news conference by the two chief negotiators -- Israeli Interior Minister Yosef Burg and Egyptian Foreign Minister Kamal Hassan Ali -- following two days of mediation here with President Carter's special Mideast envoy, Sol. M. Linowitz.

The decision was welcome news to U.S. officials, who consider the autonomy talks vital to Carter's hopes for progress toward Middle East peace under the U.S.-sponsored Camp David accords.

Neither Burg nor Ali gave any sign of change in the hard-line negotiating positions that have caused the talks to drag on for more than a year without any real progress toward creating & limited self-government system for the 1.1 million Palestinian inhabitants of the Israeli-occupied West Bank and Gaza Strip.

In their joint public appearance, though, the two ministers joked and bantered in a relaxed, friendly manner that left the impression of a potentially new upbeat swing in the strained relations between their governments.

Sources familiar with the behind-the-scenes discussions here said that these, too, were characterized by a spirit of good feeling and a desire to make a new try at mutual accommodation.

As a aresult, the sources added, there was a feeling among all the participants that what one called "the atmospherics of the situation" might be improving to the point where progress toward an autonomy accord might become possible.

The knegotiations, which had a May 26 target date for completion, were halted when Egyptian President Anwar Sadat became angered by the introduction of legislation in the Israeli parliament that would declare Jerusalem an undivided city and the permanent capital of the Jewish state.

Under the Camp David accords, the status of Jerusalem, which borders the West Bank, is to be decided at a later stage of the peace process. However, it became an issue in the autonomy talks because of Isreali and Egyptian disputes about whether the approximately 100,000 Palestinians living in East Jerusalem, captured and annexed by Isreal in 1967, should be allowed to vote for the self-governing authority on the West Bank.

Some sources involved in the negotiations believe that Sadat either overreacted on the Jerusalem issue or used it as a convenient way of diverting attention from the fact that an agreement could not be reached by May 26.

In any case, several sources said, most of the three-corned bargaining of the last six weeks involved finding ways to enable Egypt to slide back into the negotiations in face-saving stages.

In that respect, the sources said, Burg, during the talks here, went to great lengths to assure the Egyptians that the pending Israeli legislation did not have the backing of Prime Minister Menachem Begin's government and is not an Israeli ploy to foreclose future discussion on Jerusalem.

Ali is known to have relayed these assurances to Sadat by telephone when the negotiators met with Carter at the White House on Wednesday, and Sadat is understood to have given to go-ahead for renewed talks.

Some sources said another key factor in the success of the talks here appeared to be the Begin government's concern over dwindling support for Israel's position in Western Europe and among American-Jewish leaders.

As a result, the sources said, the Israelis, while not making any concessions, seemed eager to demonstrate that they are not dragging their feet on autonomy and are willing to keep trying for an agreement.

Linowitz revealed that when the talks resume they will not follow the pattern of marathon bargaining sessions by the top negotiators that was being employed before the mid-May breakoff. Instead, he said, for the next month or longer, the burden will be carried by committees of ministers and experts from the two countries who will attempt to find ways of narrowing differences on the major issues.

He identified those groups that are to begin work in Cairo next week as a legal committee to discuss the powers of the self-governing authority, an economics committee to handle questions such as trade, customs and possibly the especially sensitive issues of land and water rights, a committee to deal with mechanics of electing the self-governing authority and a ministerial team to make a new try at sorting out responsibilities for security in the disputed territories.

The sources said the idea is for the committees to try to isolate points of agreement and prepare options and recommendations that then can be taken up by Burg, Ali and Linowitz for further negotiation.

If this plan proceeds effectively, the sources said, the three top negotiators tentatively hope to resume face-to-face bargaining around mid-August, probably in Cairo.