The truce between Israel and Hamas is well into its fourth and potentially final day and there is mounting pressure on both sides to extend the pause in fighting.

Since Friday, Hamas has so far released 58 hostages, and Israel has freed 117 Palestinian prisoners from its jails.

But while Israel and Hamas may both be willing to extend the truce, doing so will be fraught with difficulties.

Logistical problems: Not all of the roughly 240 people taken into Gaza during the October 7 attack on Israel are, or were, being by Hamas, the militant group that launched the assault. More than 40 of the hostages are being held by groups other than Hamas, a diplomatic source briefed on the negotiations told CNN.

CNN has previously reported that between 40 and 50 hostages were held by Palestinian Islamic Jihad or other militant groups.

The truce agreement requires Hamas – and not another group – to hand over hostages in exchange for Palestinian prisoners. And so even if Hamas is willing to extend the truce, it may struggle to locate additional hostages. Coordinating their release may also be difficult, as communications in Gaza have been degraded by Israeli airstrikes.

Qatari Prime Minister Mohammed bin Abdulrahman Al-Thani – who helped broker the initial agreement – told the Financial Times that any extension to the fighting rests on Hamas being able to find more hostages.

“If they get additional women and children, there will be an extension,” Al-Thani said, adding that one of the purposes of the truce was for Hamas to “search for the rest of the missing people.”

Strategic problems: Extending the truce in exchange for the release of more hostages could also pose strategic problems for both Israel and Hamas.

For Hamas, the holding of hostages presents the only real leverage they have over Israel. The promise to release hostages has been the only thing that caused Israel to relent in seven weeks of fighting.

Hamas may soon up its price, demanding that the pauses in fighting be longer, or that the number of Palestinian prisoners released be greater, in exchange for the release of Israeli hostages. There is likely to be a limit to the number of hostages Hamas will be willing to free, since it will be unwilling to surrender the leverage it has over Israel.

For Israel, the truce agreement has allowed it to take steps toward achieving one of its war aims: Securing the release of Israeli hostages. But extending the truce further might make its ultimate war aim – of destroying Hamas – harder to achieve.

Releasing all the hostages was found to be a more important war aim than toppling Hamas, according to a survey of Israelis carried out by the Israel Democracy Initiative before the announcement of the truce agreement last week. But the Israeli government has stressed it is committed to achieving both aims.

Every day there is a pause in fighting gives Hamas more time to regroup, ahead of a potential expansion of fighting into the south of the Gaza Strip. Under the initial truce agreement, Israel and the United States agreed to pause surveillance drone flights over Gaza – something Israel was reluctant to do, since it would mean losing track of the movements of Hamas fighters.

And so, while extending the truce might further one of Israel’s war aims, it delays and potentially frustrates the other.

CNN’s Becky Anderson contributed reporting to this post.

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