JERUSALEM (CNN) -- Nearly 1,600 people crossed the Gaza-Egypt line in both directions on Saturday, passing through the first-ever Palestinian-controlled international border, according to a European Union spokeswoman, who said the "process has gone very smoothly.""We are extremely pleased with the way the crossing has been taking place," said Cristina Gallah, spokewoman for European Union foreign policy chief Javier Solana, who's in Barcelona for the Euro-Mediterranean summit.The Rafah Crossing, a main crossing from southern Gaza into Egypt, opened to the public on Saturday. Gallah said that "1,587 people have been able to cross the border in both directions, and the process has gone very smoothly and we consider it a success." Although the crossing did not open until noon, and then only for four hours, some arrived at 6 a.m. (Watch as the border is opened -- 1:59)Video showed people walking through metal detectors, getting their belongings scanned, then standing in line to have their passports stamped.Gaza no longer a 'big prison'On Friday, officials held ceremonies to mark the opening, with Palestinian Authority President Mahmoud Abbas taking the first steps over it -- the first time a Palestinian crossed an international border under Palestinian control."The opening of this border is important," he said, "because it means the Gaza Strip will not be a big prison."The crossing was closed in September as Israel withdrew its forces and settlers, ending its 38-year occupation of Gaza.Intense U.S.-led negotiations earlier this month led to the deal for the border to be put under Palestinian control.E.U. monitorsWhile the Rafah Crossing is officially under Palestinian control, dozens of monitors from the European Union will be there for at least the next 12 months with the final say in any dispute about who and what is allowed in and out of the territory.The Israelis will also be closely watching via closed-circuit television.Those lining up Saturday included people wanting to see relatives, students and some seeking medical treatment. Many, however, just wanted to cross the border -- some for the first time ever. Under Israeli control, Palestinians could not be sure when or for how long the crossing would be open. In addition, sometimes Palestinians were turned back or questioned for hours. Israelis frequently closed the control for security reasons.Most residents only needed a Palestinian ID, although some Palestinian men between the ages of 18 and 40 needed a visa.With Gaza no longer under Israeli occupation, open and free borders are considered by most observers crucial for the impoverished Gaza economy to grow.E.U. Middle East envoy Marc Otte said he hopes the change of control will "open the door" for Palestinians and their future in the territory."It's a historic moment," he said. "For the first time, the Palestinians will be in control of their borders. We consider that extremely important, because not only will it signify for the people a huge change in their lives to travel freely, it's freedom. It's opening."Officials said the crossing will eventually operate 24 hours a day.U.N. Secretary-General Kofi Annan praised the opening. In a written statement, a spokeswoman said Annan "appreciates the important decision made by the government of Israel to open the crossing" and extended thanks to those who made it possible.The deal that led to Friday's historic changeover was announced earlier this month by U.S. Secretary of State Condoleezza Rice during a trip to the region to mark the 10th anniversary of the slaying of Israeli Prime Minister Yitzhak Rabin. Rice oversaw all-night negotiations on the topic, staying a day longer than scheduled to encourage the breakthrough.Palestinians pushed for relaxing Israel's border restrictions to help the region's ailing economy, while Israel wanted measures in place to protect against terrorism.Under terms of the agreement, any disputes between Israelis and Palestinians will be mediated by the E.U. If Israelis, for instance, believe weapons are being smuggled across the border, they would protest to the E.U. If the E.U. believes the Israelis have a case, the border will be closed.The deal also includes construction of a Gaza seaport, and will allow Palestinians to travel between the West Bank and Gaza in bus convoys through Israel.--CNN correspondent John Vause contributed to this report