The rockets hit Israel's Eilat and Aqaba in Jordan, where one person was killed. Officials from both countries blamed Islamist militants in the Egyptian Sinai desert.
The Israeli Tourism Ministry objected to singling out Eilat for precautionary advice but not Aqaba.
"This advisory gives a prize to terror and undermines regional stability and the sense of security that Israel gives to everyone who enters the country," it said.
"Differentiating Israel from its neighbor that actually suffered loss of life is improper and lacks balance." Eilat and Aqaba are side by side on the Red Sea at the southern tips of both countries.
After the rocket attack on Aug. 2, the US Embassy in Jordan said travel to Aqaba "is discouraged for the next 48 hours," while the embassy in Tel Aviv suggested visitors to Eilat know the location of the nearest bomb shelter.
When the 48-hour period expired however no new statement was issued for Jordan, yet travelers to Israel were once again "advised to ascertain the location of the nearest bomb shelter," in a statement Aug. 5.
The Monday statement said Tourism Minister Stas Misezhnikov requested a meeting with US Ambassador James Cunningham. The embassy said he was out of the country and had no further comment.
There was also no immediate comment from the US State Department.
