Beirut — Two breakthroughs have heightened hopes for Lebanon's ''national reconciliation dialogue,'' scheduled to begin this week:
* For the first time since war began to rip Lebanon apart in 1975, rival factions sat down at the peace table last Thursday. Although a full week had been allotted for the preparatory talks, six factions and the government agreed in a single seven-hour session on an agenda for the many complex issues to be brought up at the conference.
* After 13 meetings, a security committee, comprised of the Lebanese Army and the three major militias involved in fighting over the past two months, agreed on a plan to monitor the country's fragile, three-week-old cease-fire. Formal invitations were extended Sunday to Greece and Italy to send a total of 800 troops to patrol the volatile Shouf mountains.
Progress on both the political and military fronts was vital. Specifically, there were fears the truce would collapse because of repeated daily violations, preventing Lebanon's 12 warlords from ever getting to the negotiating table. And symbolically, it was needed as an indication that rival groups could come to terms with each other.
Khalil Makkawi, chairman and government representative at the political talks , said, ''This joint effort, exerted and finalized in one session, is proof of the determination of all the participants to build in confidence the new Lebanon we all aspire to.''
This now opens the way for the conference to begin Thursday to find means of ''delivering Lebanon from its crisis,'' in the words of the official invitation extended by President Amin Gemayel. The only outstanding issue is the venue. This is largely due to personal security concerns by the opposition National Salvation Front members over attending meetings at the proposed Baabda presidential palace which is in predominantly Christian east Beirut.
But warnings are still coming from several quarters against premature optimism about the prospects of finally ending eight years of chaos and warfare. The Arabic daily newspaperAs Safir said in a front-page editorial: ''Many Lebanese feel the solid basis for the cease-fire and the proposed national dialogue is still missing.''
The delicacy of the situation was reflected in the death of a fifth American marine Friday when the 1,600-man US contingent came under sniper fire at positions near Beirut airport. ''It was an obvious attempt to draw us into conflict,'' said a Marines spokesman. The Marines, who recently added 400 troops to their onshore presence, also came under fire Saturday. Marine sharpshooters claimed to have killed several snipers.
The shots came from a predominantly Shiite Muslim neighborhood under the control of the anti-government Amal militia. But Amal denied it was responsible for the shooting, claiming Amal fighters were also coming under attack by unidentified gunmen who were intent on heightening tension on the eve of peace talks.
Western sources said preliminary investigations gave some credibility to the Amal claims. One said, ''There is someone out there trying to stir up trouble.''
Diplomats contend there are many parties in Lebanon, such as the small pro-Iranian ''Hizbillah'' Shiite militia, which oppose a national conference that will attempt to find a new formula of power-sharing among Christians and Muslims and guarantee future peaceful co-existence. ''It is in their interests to continue to harass both the MNF (multinational peacekeeping force) and the groups who will be going to the talks,'' said one envoy.