Training programme
Political sources said Olmert would refrain from going after senior Palestinian faction commanders or political leaders.
The Israeli military recently completed a training programme to prepare ground forces for a land offensive against fighters in the territory should the government give the green light, Israeli security sources said.
But one source said Olmert, his popularity flagging since last year's inconclusive Lebanon war, is not interested in a massive assault at this time.
His position could not have been strengthened by news on Wednesday that the state comptroller had recommended that the attorney-general's office launch a criminal investigation into a business deal by Olmert conducted before he become prime minister.
Micha Lindenstrauss concluded that there was a possible conflict of interest in a multimillion-shekel deal Olmert was involved in while minister of industry and trade in a previous government.
Lindenstrauss has clashed with Olmert in the past, and his recommendation on Wednesday is not binding.
Revenge for deaths
The Izz al-Din al-Qassam Brigades, Hamas' armed wing, launched the rockets on Tuesday after Israeli soldiers killed nine Palestinians in Gaza and the occupied West Bank earlier in the week.
On Tuesday, Mahmoud Abbas, the Palestinian president, had urged Israeli restraint.
Speaking in Rome he said: "The violation of the truce is an exceptional event that will not last. "I take this opportunity to appeal to Israel to show the necessary self-control so that this will not happen again."
The Palestinian government, which Abbas' Fatah faction jointly runs with Hamas, called for the ceasefire to remain in place.
"The government is interested to keep the ceasefire and the calm and we are trying, through consultation and discussion with the Palestinian factions, to take a position in order to protect our people," said Ghazi Hamad, government spokesman.
In Gaza, a Palestinian official said on Wednesday that an Egyptian security team held separate meetings with Hamas and the Islamic Jihad group and stressed the need to restore calm to avoid giving Israel a pretext to mount a ground offensive.