One man has been killed and three other people injured when a rocket landed in the Jordanian port city of Aqaba, reports say.
According to Israeli police, the rocket was targeted at the nearby Israeli resort of Eilat and was one of at least five fired from Egypt's Sinai desert.
Egypt has denied that its territory was used to launch the apparent attack.
Rocket attacks on Israel usually come from Gaza and it is rare for such an attack to come from the Sinai desert.
Analysis/ Wyre Davies/ BBC News, Jerusalem
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Although militant activity against Eilat and other "targets" in southern Israel is less frequent than elsewhere, the area is Israel's vulnerable, soft underbelly.
Despite devastating bombing campaigns against Israelis and foreigners a few years ago, the region remains popular.
Earlier this year, intelligence reports that Islamic militants in the Sinai were planning to abduct tourists brought a warning from Israel that its nationals should avoid travelling there. While many ignored that advice, thousands are holidaying in Eilat.
Given the geography of the region - with the borders of Israel, Egypt and Jordan converging at the head of the Gulf of Aqaba - Eilat is nonetheless vulnerable to attack from militants operating in the Sinai.
Israel believes there is a growing problem in the area, with increased militant activity, weapons smuggling and illegal immigration. Hence, Israel is building a huge fence along its border with Egypt and has urged the Egyptian authorities to deal with militant groups operating from its territory.
Jordan's Interior Minister Nayef Qadai earlier told the AFP news agency: "A Grad rocket fell in the street in Aqaba, near to the Intercontinental hotel, destroying two cars and injuring four people, one of them seriously."
But later a security official said a 51-year-old taxi driver had died as a result of his injuries.
Israeli media and police reported that some of the rockets fell into the Red Sea and others in open spaces near Eilat. There were no casualties there as a result of the apparent attack.
Eilat, which is a popular tourist resort, has largely been spared from rocket and other attacks.
In April, rockets were fired toward Eilat and Aqaba from Egypt's Sinai peninsula, an area from which Islamist militants have operated in the past. No-one was injured in that attack and the source of the firing was never established.
Eilat was hit in January 2007 by a suicide bomber, killing three people.
Israel has recently warned of increased militant activity in the Sinai peninsula and has advised its citizens against travelling there, says the BBC's Wyre Davies in Jerusalem.
Hamas home hit
An Egyptian official said his country had a heavy security presence in the Sinai peninsula, particularly close to the border, and that no suspicious activity had been reported anywhere in the area.
However, the Egyptian denial will be viewed sceptically by those who know the area, our correspondent says.
The government is in dispute, and sometimes conflict, with the Bedouin who live there. The Bedouin use their local knowledge to engage in widespread smuggling and are suspected of having helped those who carried out previous attacks in the area, he says.
Earlier on Monday, a large explosion at the Gaza home of a senior Hamas commander injured more than 20 people. Israel has denied any involvement.
Hamas sources told the BBC the blast hit the home of Alaa al-Danaf. He reportedly survived the blast unharmed, but his brother Abed was injured.
The explosion destroyed the house and badly damaged several nearby houses.
On Friday and Saturday night, Israeli planes launched air strikes against Hamas positions in Gaza, killing one person.
Israeli said this was in retaliation for an earlier attack from within the Palestinian territory when a rocket landed in the Israeli city of Ashkelon, without causing serious casualties.
