Israeli Prime Minister Menachem Begin proposed to President Carter yesterday that Egypt and Israel immediately begin six weeks of nonstop negotiations in the Middle East in an effort to reach agreement on the future status of Israeli-occupied Arab lands.

Informed sources said Begin, here for two days of White House talks, suggested that a marathon effort might help the U.S.-mediated negotiations achieve their May 26 target date for an accord on self-government for the 1.2 million Palestinian inhabitants of the West Bank and Gaza Strip.

In proposing intensified talks, the sources said, Begin was picking up on an idea that surfaced last week during Carter's separate meeting with Egyptian President Anwar Sadat.

Sadat and Carter favored having the three principal negotiators -- U.S. special ambassador Sol M. Linowitz, Egyptian Prime Minister Mustafa Khalil and Israeli Interior Minister Yosef Burg -- meet here later this month for extended talks.

However, the sources said Begin, who is unenthusiastic about having the negotiators meet in Washington, suggested that the talks alternate between Tel Aviv and Alexandria, Egypt.

According to the sources, Carter expressed interest in the idea, but told Begin they would have to ask Sadat whether Egypt is willing to keep the negotiations going in the Middle East. Sources said last night that Sadat's response is expected today.

The sources said Begin pointed out that only 40 days remain until May 26. As a result, Begin reportedly said he was willing to start a new 20-day negotiating round immediately in Tel Aviv and then move to Alexandria for another 20 days.

The autonomy talks already have been alternating between these two sites, but have made almost no progress in the 10 months since they began. The principal reason for moving them here, as Sadat wanted, would have been to allow Carter and Secretary of State Cyrus R. Vance to play an active mediating role as they did during the Israeli-Egyptian peace talks in Washington during late 1978 and early 1979.

However, the Israelis are understood to have balked at making Washington the new site for the talks -- in part because they fear that negotiations in the shadow of the White House would put them under too much U.S. pressure, and in part because Begin's cabinet does not want Burg or Foreign Minister Yitzhak Shamir to be far from Israel for an extended time.

That factor is especially important to the Jerusalem policy of keeping tight control over Israel's negotiating position. When the peace talks were held here in 1978 and 1979, they had to be interrupted at several critical points while the Israeli negotiators went home to confer with the Cabinet and receive new instructions.

The sources said that yesterday's two lengthy meetings between Carter and Begin took place in "a very cordial atmosphere that went very deeply into the substance" of what should be included in the autonomy agreement.

However, the sources did not disclose whether the talks produced any significant compromise ideas for bridging the gap between Egypt's demand, that the Palestinians be given a self-government system almost completely autonomous from Israel, and Israeli insistence on severly limiting the autonomy of the occupied territories to prevent their becoming an independent Palestinian state.

In addition to this fundamental problem, the negotiations have been snagged on other controversial issues such as Israel's right to keep security forces in the occupied territories, control over water and land resources, and the degree to which the agreement will apply to Palestinian residents of East Jerusalem.

A further complication has been Israel's insistence on establishing Jewish settlements in the occupied territories, despite repeated U.S. protests. However, the mandate given Begin by the Israeli cabinet for the White House talks precluded discussion of any topics not specifically covered by the 1978 Camp David accords.

Since the Camp David agreement, which is the basis for the autonomy talks, does not mention the settlements, the Israelis have contended that they cannot be discussed in the Carter-Begin meetings. The sources said they were not mentioned in yesterday's talks.

At a White House dinner last night, Begin stressed that his country is a true ally of the United States but must be concerned about its own security.

"There are two categories of American allies," Begin said in his toast. "The first are allies; the second are reluctant allies. Israel is among the first. . . . In good and in bad days, we stand by you and are with you. . . ."

But, in a reference to the possible creation of a Palestinian state on Israel's border, Begin added that the United States must never adopt a policy threatening Israel's security.

An Israeli newspaper, the English-language Jerusalem Post, reported in a dispatch from Washington yesterday that former secretary of state Henry A. Kissinger, in an off-the-record talk Saturday to a dinner meeting of American-Jewish leaders, severely criticized the autonomy talks on the ground that they would lead to creation of a radical Palestinian state.

According to the Jerusalem Post article, Kissinger said Begin should insist on redefining the Camp David accords in a way that "would more forcefully preclude the development of an independent Palestinian state."

Kissinger is traveling in Europe. In response to questions about the article, he authorized a spokesman in his Washington office to deny "vehemently" that he is critical of the Camp David agreement or believes that the negotiations are dangerous to Israel.

The spokesman said Kissinger is on record as opposing an independent Palestinian state. But, the spokesman added, Kissinger "strongly supports the Camp David agreement and the current negotiations being conducted by President Carter."