JERUSALEM, Jan 4 (Reuters) - Israel has set several goals for its military offensive in the Hamas-ruled Gaza Strip.

Government officials, speaking to Reuters on condition of anonymity, said they were:

- To weaken Hamas substantially by killing its fighters and destroying its rocket stockpile. Israel says it has already dealt a major blow to Hamas on both counts.

- To establish Israeli deterrence so that Hamas will be more wary of firing cross-border rockets again. Hamas has so far sounded defiant, saying the fighting with Israel had only begun.

- To win international backing for new security arrangements along the Egyptian-Gaza border to prevent Hamas from rearming. Israel has been bombing smuggling tunnels. European powers have proposed deploying international monitors that could man the Rafah border crossing, if it is reopened. Israeli officials have suggested building an underground wall on the Egyptian side of the border, possibly with U.S. help.

- While cool to the idea of a formal ceasefire that could bind Israel's hands and provide Hamas with a measure of legitimacy, Israel wants to restore calm through "understandings", reached through a third party, under which both sides would hold their fire. Such understandings might give Israel more leeway for future military action against Hamas if rocket fire resumes. (Reporting by Adam Entous; Editing by Dominic Evans)

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