The Israeli military was not giving out details of its preparations, but television reports showed soldiers repairing fences and bulldozers digging trenches along the borders in the north. On Thursday, Prime Minister Benjamin Netanyahu said he had instructed Israeli forces to act with restraint, but also with determination, to protect Israel’s sovereignty and borders. According to reports from Lebanon, activists there canceled plans to march to the Israeli border after the Lebanese authorities declared the border area a closed military zone.

On Saturday, Palestinian officials signaled another possible source of pressure on Israel, saying they would accept a French proposal to attend a peace conference in Paris next month with the aim of restarting negotiations based on the broad principles laid out by President Obama last month. Mr. Obama said that talks should be for a future Palestinian state based on the 1967 lines with mutually agreed land swaps. He also suggested that talks should focus first on the issues of borders and security, and deal later with the contentious issues of the status of Jerusalem and the fate of Palestinian refugees of the 1948 war and their descendants.

The Palestinian president, Mahmoud Abbas, said that in principle, the French proposal was acceptable. He told the Reuters news agency on Saturday that under the plan, neither Israel nor the Palestinians would carry out “unilateral actions.” The Palestinians have demanded a freeze in Israeli settlement building, while the Israelis oppose Palestinian plans to bypass negotiations and seek recognition for statehood at the United Nations this fall.

There has been no public response to the French plan from the Israeli side, but Israel has previously rejected talks based on the 1967 lines. Moshe Yaalon, the minister for strategic affairs in the Israeli government, told Israeli television on Saturday that Israeli leaders would discuss the French proposal this week.

In a sign of growing frustration in Gaza, travelers tried to force their way through a crossing on the border with Egypt that was temporarily closed on Saturday, a week after Egypt declared it open permanently in a move hailed by Palestinians as an end of the Israeli-led blockade of the coastal enclave.