JERUSALEM, April 5 (Reuters) - A rocket fired from Egypt's Sinai desert struck the southern Israeli city of Eilat on Thursday causing no casualties or damage, Israeli police said.

The head of Eilat police, Ron Gertner, told Army Radio that explosions were heard in the holiday resort soon after midnight. Police found the remains of one rocket in a construction site, about 400 metres from a residential area.

Asked if the rocket was fired from Sinai, Gertner said: Based on our working assumptions and the (rocket) range, yes. He added that police were searching for more rockets that may have landed.

The rocket attack came on the eve of the Jewish Passover holiday when the Red Sea resort is expected to be full of vacationers.

Officials in Israel are concerned that the Sinai desert has become a flourishing base for Islamist militants since former Egyptian President Hosni Mubarak's downfall last year.

The Israel-Egypt border had been relatively quiet since the two countries signed a peace agreement in 1979. But Israel says that since Mubarak was overthrown, Cairo has lost its grip on the Sinai and militants are exploiting the lawlessness.

Last August armed infiltrators killed eight Israelis on the Egyptian frontier. Israel's forces, repelling the gunmen, killed five Egyptian border troops. Israel said the attack was orchestrated by Palestinian militants.

To fend of infiltration, Israel has been building a fence along the southern border which it hopes to complete by the end of 2012. When it is finished, the barrier will run most of the 266 km (165 miles) from Eilat on the Red Sea's Gulf of Aqaba up to the already-closed Gaza Strip on the Mediterranean. (Writing by Maayan Lubell; editing by Crispian Balmer)