Continued difficulties for the United States in the Middle East were highlighted this week on several fronts. Regional stability is at stake, especially the success or failure of President Reagan's quest for a withdrawal of foreign forces from Lebanon and a permanent peace between Israel and its neighbors.
* Perceiving threatening moves from Libya near the Sudan border, the US dispatched radar surveillance planes to Egypt, the only Arab country that has signed a peace treaty with Israel. It also shifted the aircraft carrier Nimitz from its post off Lebanon to the central Mediterranean, where US Navy fighters shot down two Libyan jets two years ago.
* Defense Secretary Caspar W. Weinberger confirmed to members of Congress that there is tension between the US and Israel over the sharing of intelligence data obtained as a result of the war in Lebanon last summer. The US has rejected an Israeli offer to share data, Mr. Weinberger said, because Israel is demanding too much in return.
* Secretary of State George Shultz urged Washington lawmakers to approve increases in foreign aid, much of which will go to the Middle East, as an investment in world stability. While Israel still would get more military and economic aid per capita than any other country, lawmakers are sure to oppose administration plans to reduce some aid to Israel.
Part of the US attempt to woo Arab nations to a more moderate position regarding Israel involves help in preventing what is seen here as Libyan leader Muammar Qaddafi's attempts to ''destabilize'' some countries in the region. Egypt, Tunisia, and Sudan - all of which share borders with Libya - receive US military aid.
This week's US military activity related to Libya is the sharpest since mid- 1981. Then the US challenged Libya's contention that the Gulf of Sirte is part of its territorial waters, and destroyed two attacking Libyan aircraft. A few months later, AWACS aircraft were sent to Egypt after the assassination of President Anwar Sadat, when it appeared to US officials that Colonel Qaddafi was taking advantage of regional instability to attack Sudan and threaten Egypt.
Earlier this month, Libya began building up military forces near its borders with Egypt, Sudan, and Chad. In response, Egypt moved air force units closer to that area.
While the US holds regular military training exercises in the region, officials acknowledge that the decision to deploy four AWACS aircraft to work with the Egyptian Air Force was made within the past few days.
''These exercises always have a joint benefit,'' said a senior administration official, ''to improve readiness, and if they have the result of reducing tensions, so much the better.''
The carrier Nimitz, whose main task recently has been to back up US Marines in Lebanon, steamed west to represent the rattle of another US saber. Air operations were conducted in the Mediterranean north of Libya, but, by design, not close enough to provoke an attack.
While the US was thus demonstrating its support for moderate Arab states this week, it was also sending firm signals to Israel.
Secretary Weinberger told the House Budget Committee there was ''unanimous consent'' among Pentagon, State Department, and National Security Council officials that what Israel was demanding in return for intelligence information ''was not . . . in the best interests of the United States.''
Israel insisted that such data not be passed along to US allies, and that any technology developed as a result not be made available to third-world countries without Israeli approval, Weinberger said.
As outlined by Secretary Shultz, US aid to Israel for the coming fiscal year would require that more be repaid than in the past. This would be the second year that the Reagan administration wants to reduce grants to Israel and increase loans, in effect cutting aid. Last year, over administration objections , Congress increased aid to Israel.