All five of the wounded tourists were from Ecuador, said Foreign Ministry spokeswoman Jill Reinach. Rescue workers said one woman was gravely wounded.
Meanwhile, Egyptian mediators and the Palestinian prime minister traveled to the Gaza Strip on Wednesday to try to persuade militants to halt attacks on Israel, and Palestinian police arrested a suspect in the killing of two Israeli soldiers.
Officials said the attacker concealed himself in the back of a truck approaching the border, leapt out and opened fire before he was shot by Israeli security personnel.
The incident occurred at the Rabin terminal, an open-air checkpoint near Eilat, a Red Sea tourist town next to the Jordanian resort of Aqaba.
There was no immediate claim of responsibility. Asma Khader, a Jordanian minister, said the gunman was a truck driver who was not believed to be part of any organized armed group.
"Jordan regrets the incident and ... condemns acts of violence which target civilians," said Asma Khader.
CBS News Correspondent Robert Berger reports Israeli officials say the incident points to lax security on the Jordanian side of the border.
Jordan and Israel established diplomatic relations in 1994. Incidents of cross-border violence are rare, although in 1997, seven Israeli schoolchildren were killed by a Jordanian soldier in a border area near the northern Israeli town of Beit Shean.
Israeli sources said Palestinian Prime Minister Ahmed Qureia and Israeli Prime Minister Ariel Sharon would meet next week, and expressed hope for Qureia.
He "will not be a puppet nor a rag doll nor a spitting image of Yasser Arafat," said a senior Israeli official. "We don't know if he'll be good or bad, but clearly he's a very independent fellow."
Qureia, who took office last week, said his first priority is to get the militants to agree to a truce, and then bring Israel into the accord.
There were signs that Israel is softening its position, in part because Sharon is under growing pressure at home and abroad to end the deadlock.
In the past, Israel had refused to consider a truce until Palestinian security forces begin dismantling armed groups — a requirement of the road map. Palestinian leaders have balked, saying they will not use force against the militants for fear of triggering internal fighting.
In recent days, Israeli officials have indicated they are willing to give a truce a chance, for a limited period, without insisting on a crackdown on militants.
The senior Israeli official, briefing reporters accompanying Sharon on a trip to Italy, said Israel is willing to stop most targeted killings of Palestinian militants if Qureia obtains a truce pledge from the armed groups. This would meet a key demand by the militants, who say they will only halt attacks if Israel promises to halt military operations and the deal is backed by international mediators.
The Israeli official said militants planning or carrying out attacks would still be targets. He also stressed that Israel would never recognize a Palestinian state if the violent groups are not dismantled.
A unilateral cease-fire declared by the militants in June broke down after several weeks, in part because Israel continued to carry out arrest raids, some of them deadly, and militants responded with revenge attacks. At the time, Israel said the cease-fire was an internal Palestinian matter.
Islamic Jihad spokesman Nafez Azzam said the group welcomed dialogue with Qureia and the Egyptians, but said a cease-fire would depend on Israel.
"Any new proposal or any initiative should be guaranteed that the enemy will be committed to halt their aggression against our people and not to violate the hudna (cease-fire)," he said.
But the Al Aqsa Martyrs' Brigades, a violent group loosely affiliated with Palestinian leader Yasser Arafat's Fatah movement, appeared to rule out a cease-fire. "We are committed to continue resistance and confronting the occupation all over Palestine, as long as there are soldiers, settlers and occupiers on the land of Palestine," the group said.