A Jordanian truck driver opened fire on a group of tourists at a border crossing near Israel's Red Sea resort of Eilat, wounding four other people before he was shot dead on Wednesday.
The gunman was killed by Israeli security personnel.
The attack could further harm Israel's already devastated tourism industry after three years of the intifada, or Palestinian uprising, against Israel’s occupation.
Jordanian officials condemned the attack and said the gunman, who came from a predominantly Palestinian town, was not connected to any resistance group.
But Israeli Defence Minister Shaul Mofaz called the attack "part of the recent long and painful string of terror attacks in which world terror groups were involved."
Israeli officials said at least four Ecuadorean Christian pilgrims were wounded.
One of them, a 33-year-old woman, died from a head wound nine hours later at Soroka hospital in Beersheba, said a hospital spokesman.
The tourists were part of a group of 39 Ecuadorean pilgrims who were touring Middle East holy sights, said Yossi Zeldish, an official from Palmer Tours who organised their trip.
Israelis and tourists take cover
at the Rabin terminal
The pilgrims were returning from sites in Jordan and were due to cross from Eilat into Egypt on Thursday to visit St. Catherine's Monastery in the Sinai desert.
The Israeli tourism ministry said Israel and Jordan had agreed to intensify security at the border and increase joint patrols.
The governor of the neighbouring Jordanian port of Aqaba said supervision would be stepped up to keep weapons out of the area.
Jordanian minister of state Asma Khader said her government condemned the incident.
She said the gunman was a resident of Zarqa, 27km northeast of the Jordanian capital Amman, and that Jordanian troops had searched his home. However, Khader said that no arrests had been made.
“Preliminary information indicates that it was an individual and not an organisational act," she said.
Eilat a city of 42,000 - with attractions including coral reefs, deep-sea diving, dolphin petting, casino boats and discotheques - attracts tens of thousands of tourists year-round, especially from Europe.
Jordan and Israel established diplomatic relations in 1994, and there have only been a handful of incidents of cross-border violence since then.
In the deadliest instance, a Jordanian soldier shot and killed seven Israeli schoolgirls in 1997 near the northern Israeli town of Beit Shean.
The most recent incident was in March 2002, when Israeli soldiers killed four armed resistance fighters. Jordanian forces killed two others.
In other news, a female Israeli soldier, wounded in a bomb attack on a military base near Tel Aviv, has died of her injuries.
The resistance attack at Tzrifin was followed a few hours later by another bombing at a cafe in the German Colony area of Jerusalem.