Cabinet Secretary Oved Yehezkel began polling the government ministers Tuesday in order to secure their consent for an additional draft of 2,500 reserve soldiers as part of Operation Cast Lead in the Gaza Strip.
The cabinet approved the drafting of 6,700 reservists on Sunday.
The new draft bid is said to be taking place amid a meeting between Prime Minister Ehud Olmert, Defense Minister Ehud Barak and Foreign Minister Tzipi Livni, regarding the Gaza offensive.
The defense establishment reportedly recommended the National Security Cabinet explore a 48-hour "humanitarian ceasefire" in order to better assess the situation in the Strip – an option Olmert is reluctant to apply.
Barak instructed Yehezkel to call all the ministers in an effort to have the bid approved overnight. Should a new draft order by granted, the troops would reinforce the existing fighting units, in preparation for a possible ground incursion.
Earlier, a senior Hamas source confirmed that the organization had been approached by several international elements, relaying a ceasefire message from Israel, but the Israeli initiative, he said was rejected.
"This offer is meant to serve first and foremost the Israeli interest and help (Israel) out of the difficult situation it found itself in on the past two days. We will hold our fire only when it suits us. For now, the shahids' (martyrs) blood is preventing us from accepting this offer," he added.