The deployment of foreign inspectors at the Rafah terminal is a key element of an emerging Israeli-Palestinian deal on new border arrangements following Israel's pullout from the Gaza Strip in September.
EU foreign ministers agreed at a meeting in Brussels, Belgium, to assume third-party responsibility for monitoring the crossing, Javier Solana, the EU's security affairs chief, said.
Israel closed Rafah just before the withdrawal, citing security concerns, and the terminal has re-opened only sporadically since then to allow hardship cases through.
The Palestinians want the Europeans to serve as advisers, while Israel wants the foreigners to be in charge, with the authority to carry out arrests or confiscate luggage if necessary.
Israel is concerned about an influx of weapons and resistance fighters.
Palestinian Cabinet Minister Muhammad Dahlan accused Israel of trying to maintain a presence in Gaza despite its withdrawal.
"We don't want any foothold here," Dahlan said. "What we want is freedom of movement for passengers in and out of Gaza, and freedom of movement for goods out of Gaza to Egypt."
Touring the border, Marc Otte, the EU's Middle East envoy, said: "We are not here to control anybody. We are here to help and assist."
Reopening Rafah under Palestinian control is a crucial sovereignty issue for Gazans since it would give them authority over their borders for the first time.
Israeli-Palestinian agreements on Rafah and other crossings on the Israeli border are also necessary to rebuild impoverished Gaza.
The deployment of foreign inspectors in Rafah would set an important precedent that could be copied at a future airport and seaport in Gaza. Israel wants the Europeans there to ensure that fighters and weapons do not enter Gaza.
James Wolfensohn will remain
in the region for a week
European officials met separately on Sunday with Israeli and Palestinian officials. Palestinian negotiator Saeb Erikat said the Europeans told him the inspectors were ready to fulfil whatever role agreed to by the Israelis and Palestinians.
Later on Monday, international envoy James Wolfensohn was to chair a three-way meeting with Israeli and Palestinian officials to try to resolve the remaining disputes over Rafah.
Wolfensohn will be in the region for a week and also hopes to make progress on other unresolved Gaza issues, including improvements at crossings from Gaza into Israel. Israel is a key export market for the Palestinians.
A key issue at Monday's meeting will be Israel's demand to monitor Rafah long-distance, via computer hook-up and closed-circuit TV, Erikat said. The Palestinians reject the demand, saying the presence of European inspectors should be sufficient.
Erikat said he hoped an agreement on Rafah could be reached by the end of the week. Sharon told parliament's Defence and Foreign Affairs Committee that it was important for Israel to monitor who is passing through Rafah, said lawmaker Ran Cohen, a committee member of the opposition Yahad party.
Sharon told lawmakers that Israel must retain the right to keep monitoring, and that Israel was preparing alternate crossings under Israeli control if an agreement on Rafah could not be reached, Cohen said.
Palestinian workers at Rafah set up checkpoints on Monday and hooked up security cameras to monitor the approaches to the terminal. Dozens of Palestinian policemen took up positions along the perimeter wall and at the crossing's main gate.
Also on Monday, EU foreign ministers agreed to train Palestinian police forces for three years, beginning on 1 January. The mission is to be the 25-nation bloc's first security role in the region as part of international peace efforts.
Palestinian police will get training
for three years from the EU
Sharon, meanwhile, told lawmakers on Monday that if Hamas participates in Palestinian legislative elections, Israel will not coordinate with the Palestinians on the vote, and will make it difficult for Hamas to campaign freely.
The Palestinians say Israeli roadblocks throughout the West Bank must be lifted ahead of the 25 January election to let candidates campaign freely and permit voters to travel to rallies and the polls.
With Hamas participating, Israel will not help in the elections, and because of that, there will not be an election, even if Israel does not "intervene," prime ministerial spokesman Asaf Shariv quoted Sharon as saying.
Israel has demanded for months that Palestinian leader Mahmoud Abbas disarm Hamas if it is to take part in the election.
Abbas has repeatedly refused, saying such a confrontation would provoke civil war. Instead, he has brokered a shaky truce agreement with the resistance groups not to attack Israel and has worked to bring them into Palestinian political life by having them field candidates in the parliamentary election.