"We are troubled by the violence along the Egypt-Gaza border," Martin Nesirky, spokesperson for Secretary-General Ban Ki-moon, told reporters.
"We call for calm and respect for Egyptian sovereignty," he added.
According to media reports, Egyptian security officials said the officer was hit by Palestinian gunfire from across the border. Dozens of protesters were also reportedly hurt during the demonstrations held on Tuesday, called for by Hamas, which took over control of Gaza in June 2007 from the Palestinian Authority.
The ongoing Israeli blockade of Gaza, imposed following the Hamas takeover, has limited the amount of goods that can enter the area, triggering a humanitarian crisis for 1.5 million Palestinian inhabitants.
UN officials and aid agencies have repeatedly called on Israel to lift the restrictions so that essential supplies, including food, fuel and construction materials, can enter Gaza and to increase freedom of movement in both directions.
Just yesterday, Mr. Ban, in a phone call with Israeli Defence Minister Ehud Barak, expressed appreciation for the fact that limited amounts of glass were now being allowed into Gaza for the repair of homes but pressed for further imports of needed material for reconstruction.
"We remain deeply concerned at unsustainable conditions in Gaza and reiterate the need for the re-opening of all crossings as envisaged by the 2005 Agreement on Movement and Access," stated Mr. Nesirky.