Shifting alliances in Israel's parliament, the Knesset, today appeared to offer Prime Minister Menachem Begin's ruling Likud coalition the prospect of sounder footing and the opposition less opportunity to topple the government without new elections.

As Likud leaders continued to narrow their differences with the two-member Telem Party in an effort to bring Telem into the coalition and restore Begin's one-seat majority in the 120-seat Knesset, a member of the opposition Democratic Front for Peace and Equality (communist) party threatened to break ranks and form an independent party or quit the Knesset.

In a classic illustration of the fluid nature of Israeli parliamentary politics, Charley Biton of the four-member Democratic Front startled the opposition today by his threat to walk out amid reports he would create yet another splinter faction and align it with the Likud coalition if he negotiated a Cabinet portfolio. Biton later said he would quit his party only if his supporters in the Black Panther protest movement decided to abandon the faction.

Begin's sharp setback last month, when two Likud Knesset members, Amnon Linn and Yitzhak Peretz, bolted the coalition and joined the opposition Labor Alignment, appeared close to being offset by the entry of the Telem Party into the coalition.

Knesset sources said Telem and Likud have ironed out a common policy on the economy and opposition to relinquishing any part of the occupied West Bank and Gaza Strip, and the only remaining obstacle to a partnership is the question of Cabinet representation.

The defections by Linn and Peretz eliminated the Likud's one-seat majority last month, leaving the coalition with 59 seats, against the 56 seats on which the combined opposition could count. The swing votes were Telem's two members and three members of the nationalist Tehyia (Renaissance) Party, which split with the Likud last year in opposition to the Egyptian-Israeli peace treaty.

Begin repeatedly has said he will not head a minority government, and that if he cannot attract enough new coalition partners to comprise a parliamentary majority, he will call for new elections, possibly in November.

The Labor Alignment has sought through a series of no-confidence votes to topple the government so Labor might then attempt to form a coalition majority without having to face elections.