Egyptian and Israeli negotiators began drafting a peace treaty here yesterday after receiving a renewed public commitment from President Carter to seek regional as well as bilateral peace agreements in the strategic Middle East.

The 10-member Egyptian delegation and nine-member Israeli delegation, each made up nearly equally of civilians and military men, trooped across the street to Blair House for their first negotiating session after the presidential sendoff in the White House East Room.

A spokesman later called the first session, which covered procedural matters, "cordial, friendly and constructive, with all the delegations showing a determination to get on with the job."

Secretary of State Cyrus R. Vance and aides from the 14-member American delegation later met the Israeli team for 1 hour 45 minutes and the Egyptian team for 1 hour 25 minutes. There also was a working luncheon of all three groups.

A brief press statement late yesterday said "good progress" was achieved and separate meetings with the U.S. team will continue today.

The East Room sendoff, the Blair House site for the talks, the procedures of yesterday's deliberations, and strong words from Carter and Egyptian Minister of Defense Kamal Hassan Ali underscored in substantive as well as symbolic fashion the heavy U.S. role and responsibility for this continuation of the process begun at Camp David.

"The United States is committed without reservation to seeing this great process through until each party to the Arab-israeli conflict is at peace with all the others. Our own national interests are deeply involved," Carter declared in the opening ceremony before some 200 delegates and guests.

The president pledged to "work hand in hand with all involved parties until the job is done" and said "my own personal involvement is assured to you." The statements amounted to an open invitation to bring unresolved disputes and continuing problems to the Oval Office.

Carter dealt deftly but directly with the most troublesome issue arising from Camp David - the relationship between the Egyptian-Israeli peace agreement in the Sinai, on the one hand and the more complex arrangements to establish self-government and negotiate the future of the Israeli-occupied West Bank and Gaza Strip, on the other hand.

The talks that began yesterday will