No. Lesbian or homosexual marriage does not exist in Israel. It is possible for two Israeli lesbians or homosexuals to get married abroad, where the relevant foreign law permits marriage between parties of the same sex.  Furthermore, upon their return to Israel, this marriage can now be recognized , administratively, in Israel afterwards , following a November 2006 Israeli Supreme Court of Justice 6: 1 majority ruling. This  ordered the Ministry of Interior to register such foreign marriages, providing there is documentary proof that the ceremony was conducted and recognized according to law, where it took place.

In any case,  a single sex  couple can make a family life agreement in Israel and have it authorized at a family court.