The Carter administration sharply escalated its diplomatic and military efforts to shore up friendly governments in the Persian Gulf and Arabian peninsula region yesterday on the eve of President Carter's departure for Egypt.

In the most visible sign of the administration's growing concern, the Pentagon let it be known that Carter had ordered the aircraft carrier Constellation to leave its base inthe Philippines and to steam toward the Persian Gulf for an indefinite tour of duty.

Decisions to move the 80,000-ton carrier and to authorize a crash effort to get fighter aircraft and tanks to North Yemen now were reportedly made Monday at an emergency White House meeting devoted to the continuing fighting between North and South Yemen, and to the administration's growing concern about Soviet and Cuban involvement in that fighting.

Reports on the tone and substance of comments at the Special Coordinating Committee meeting, which Carter and Vice President Mondale attended, suggest that Carter is determined to prevent South Yemen, which the administration sees as a client of the Soviet Union, from scoring a military victory over North Yemen, a neighbor and close ally of Saudi Arabia.

"There isa feeling that Carter is drawing the line to stop the Russians and Cubans in North Yemen," said a congressional source apprised of the White House foreign policy meeting. "He seems to think the progression from Angola through Ethiopia has to be stopped here."

The meeting was chaired by Carter's national security adviser, Zbigniew Brzezinski, who has frequently called for tougher U.S. responses to deter Soviet actions in the Third World. Secretary of State Cyrus R. Vance was also present.

At a breakfast meeting yesterday, Carter briefed congressional leaders on the Yemen crisis, which erupted into border warfare on Feb. 23. South Yemeni tanks and troops have driven deep into North Yemen's border provicnes and remain there despite Arab League calls for a cease-fire and withdrawal.

The president said that a major U.S. resupply effort to make up for equipment North Yemen is losing in the fighting has begun and will continue indefinitely, according to congressional sources. Carter reportedly also spoke about providing new warplanes to Saudi Arabia as a response to the crisis, but he did not provide details.

As part of the general effort to increase the visibility of the U.S. commitment to the region, Carter told the congressional leaders that he was considering ordering an armed squadron of F15 fighters to visit Saudi Arabia soon. The administration in January sent a squadron of F15s to Saudi Arabia on a similar mission but those planes were unarmed and were used only for display.

As soon as the fighting began, Saudi Arabia approached the administration to work out a plan that would enable the Saudis to send a squadron of F5E interceptor fighters and heavyy artillery to the North Yemenis, according to administration sources.

The United Sates quickly agreed to replace the Saudi aircraft and other war materiel, but administration officials indicated yesterday that Saudi Arabia has since dropped the idea of shifting its planes and pilots into the heavy fighting.

The Saudi reticence triggered a decision by the White House Monday to start immediate deliveries of F5E fighters and long-range artillery to the North Yemenis, who have not been trained to handle these weapons, according to diplomatic sources.

With evident American approval and suggestions of cooperation, Saudi Arabia has reportedly committed itself to finding and paying pilots and advisers from other Arab nations who would fight for the North Yemenis. Jordan and Egypt have reportedly offered to send advisers to help the Norht Yemenis.

The outside Arab advisers would be seen by the administration as a counterweight to the 1,000 Soviet and 800 Cuban advisers who, in the adminsistration's view have done nothing to restrain the sophisticated tank and artillery assaults by the South Yemenis.

Administration specialists have concluded that South Yemen's offensive is aimed at toppling the pro-Saudi military government in North Yemen by totally discrediting it on the battlefield. The Aden forces would presumably then attempt to carry out an unfulfilled 1972 plan to unify the two countries.

The squadron of F5 fighters, part of which could reportedly be delivered in a matter of days, would come from a $300 million package of arms that the United States has already committed to North Yemen and which will be financed by Saudi Arabia.

Pentagon sources said yesterday that, under a $139 million contract agreed to in 1976, 7,000 shoulderfired antitank rockets were airlifted into North Yemen last week and 30 of a promised 74 Vulcan antiaircraft guns have been delivered.

These sources also disclosed that the United States is committed to replacing $8.5 million worth of military equipment that Saudi Arabia is transferring to North Yemen. Included are a dozen recolilless rifles, 26 armored personnel carriers and other tracked vehicles.

State Department spokesman Hodding Carter underscored administration concern at a daily press briefing yesterday, saying the administration has, in high-level diplomatic contacts, "encouraged the Russians to counsel moderation and peaceful resolution to this problem between the two countries." He said the security of the Persian Gulf region was a "vital United States interest."

Vance reportedly expressed that concern directly to Soviet Ambassador Anatoliy F. Dobrynin on Monday at a meeting sought by Vance and devoted entirely to Yemen. Vance reportedly asked the Russians to encourage their "client state" to withdraw its forces from North Yemeni territory immediately.

The fact that reporters were told of the movement by the Constellation and several escort ships before they left Subic Bay in the Philippines also underscored the administration's determination to be seen to be doing something now to stabilize the Persian Gulf region.

The Constellation, which carries 80 or more planes, was ordered to move toward the Indian Ocean in December as Carter sought to show support for the embattled shah of Iran. But the aircraft carrier's movement was halted after three days.

The overthrow of the shah by an Islamic revolutionary government last month -- despite Carter's strong public expressions of support for the Iranian monarch -- has raised apprehensions throughout the region about U.S. commitments abroad and appears to be a major factor in the administration's determination to make a stand in North Yemen, government sources said.