The Israeli Army is encouraging Lebanese Christian militiamen friendly to the Jewish state to carry arms and act as irregular forces in areas under Israeli occupation, a development that could prove to be a new obstacle to already difficult efforts to restore sovereignty to the Lebanese government and its official Army.

An informal military role, similar to that conferred on the Christian Phalange militia and Christian Maj. Saad Haddad's Israeli-sponsored forces in southern Lebanon, also is being allowed Shiite Moslem gunmen of the Amal organization.

Both the United States and Israel have proclaimed that a strong Lebanese government is their goal. At the same time, Israeli policy makers have spoken privately of proposals to expand the area of southern Lebanon under Haddad's control and give their ally a stronger voice in whatever Lebanese political negotiations emerge from the institutional rubble left by seven years of conflict and Israel's devastating invasion.

Underlining the Israeli objectives, Prime Minister Menachem Begin said in Jerusalem tonight that he will "not leave Maj. Haddad in the lurch."

"I think he should take part in the central government," Begin told visiting journalists. "He should be a member of the government."

The sight of irregular gunmen at checkpoints on Lebanese roads fits with the history of this troubled country since civil war broke out in 1975 and central authority crumbled. The difference now is that Israel, as the occupying force, apparently favors it, and that Phalange and Haddad militiamen are operating openly in Israeli-occupied territory, in areas that formerly were strongly Moslem and pro-Palestinian.

This suggests that Israeli goals could include establishing a Phalange military presence in traditionally Moslem areas, reaching toward Haddad's border territory, which in turn would expand northward by inclusion of Shiite villages with Amal units armed by Israel through Haddad, an Israeli military source pointed out.

The Phalange militia, which is allied with and receives arms from Israel, already controls East Beirut and Christian areas north and east of the capital. Adding it to a broadened Haddad area--controlled by Israel--would hand Israel a large portion of Lebanon guaranteed by friendly forces even if the Lebanese Army cannot take over effectively following an Israeli withdrawal.

Several developments indicate that Israel could be laying the groundwork for such a policy:

* Phalange militiamen were allowed to move into the Aley area in the hills east of Beirut along with Israeli troops who drove Palestinian guerrillas and Syrian troops eastward in heavy fighting last week. The region had been controlled for years by Druze militiamen under the command of Walid Jumblatt, Lebanon's overall leftist Moslem leader allied with the Palestine Liberation Organization.

Despite subsequent clashes between Phalange and Druze gunmen, followed by orders from Defense Minister Ariel Sharon that Israeli commanders were to prevent Phalange militiamen from abusing the Druze, Sharon did not order the Christians to leave.

* Phalange militiamen, wearing their uniforms with "Lebanese Phalange" lettered over the breast pocket, were seen by this correspondent walking freely around Sidon and entering Israeli military headquarters here. This coastal town, about 25 miles south of Beirut, traditionally has been strongly Moslem. Since Beirut's authority fell apart, it had been run by local Nasserite leftists allied with PLO commanders for the area. Before the Israeli invasion, a Phalange gunman who showed up in uniform would have been shot or arrested on the spot.

* Christian militiamen, standing alongside Israeli troops and sporting the traditional Lebanese pistol stuck in their belts, were checking Lebanese cars at a barrier at the entrance to Sidon. Their organization was not determined, but Haddad has been given authorization to help monitor the return of Shiite families from besieged Beirut back to their villages in the south. Israel has restored side arms and nominal authority to local gendarmes here, but they were nowhere in the vicinity of the checkpoint.

* Christian militiamen, apparently from the Haddad group, were strolling comfortably down the street in Tyre, a half hour drive north of the Israeli border. Tyre also had been run by a local PLO commander in cooperation with local residents until the Israeli invasion. For the last several years, its only contact with Haddad's nearby militia had been shelling exchanges.

* Haddad has been seeking to recruit Lebanese from areas under Israeli control to increase the size of his 1,200-man militia, which is supplied and paid by the Israeli Defense Ministry. His efforts have concentrated on southern Shiite villages, where local residents often were incensed at PLO abuses in their area, but also have included Tyre and Sidon.

"Haddad out of his own initiative, probably to gain power for political negotiations in Lebanon, came over," said an Israeli military spokesman describing Sidon. "We specifically did not encourage him or ask the people to join him."

The spokesman said he did not know about the Phalange militiamen in the area.

Many southern villages already have been under the protection of the Shiite militia, Amal. Israeli authorities have announced they will allow Amal militia units in the villages to retain their arms. It is unclear how this will mesh with Haddad's efforts to expand military control, but it appears to depend on his ability to get along with local Amal commanders whose areas abut his own border strip.

Haddad recently organized a ceremony with help from local Israeli commanders in the former Palestinian stronghold of Nabatiyah, seeking support from the predominantly Shiite local population, including some who recently returned from Beirut. Although the reception was friendly, Israeli officials have since reported that Nabatiyah's Shiites are less enthusiastic in private.

Haddad and the Shiites have had in common a desire to free the area from abuse by Palestinian guerrillas. But now that this shared enemy is gone, it is difficult to see much common ground between an Israeli-supported Christian officer and the Shiite farmers, many of whom look to Iran's Ayatollah Ruhollah Khomeini for political and spiritual inspiration.

Reports in the Israeli press said Haddad nevertheless has begun organizing village militias attached to the loosely structured Amal group, but supplied from Haddad's Israeli stores. The first unit has been set up in Ansar, a village north of Nabatiyah, the reports said.

Some Israeli officials recently suggested that a multinational peace force in southern Lebanon--previously a major Israeli demand--might not be necessary after all. This has led to questions whether Begin's government could be thinking of setting up Haddad and the Shiites as armed allies to police the area instead.

Israeli insistence on disarming Palestinians and their Lebanese Moslem allies in Beirut does not apply to the Christian Phalange militia, Israel's ally. This means the Lebanese Army, which is to take over in West Beirut, would remain less powerful than the Phalange irregulars in East Beirut.