According to the media reports, the decision is in line with Jerusalem's attempts to revive what was once close ties with Ankara.
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The two nations' ties have been strained since the 2010 Israeli Navy raid on the Marmara, a Turkish ship seeking to break the maritime blockade placed on Gaza. Nine Turkish nationals were killed in the raid.
The reports were not corroborated by any official source in Jerusalem.
According to the report, several Turkish building companies have specifically requested to transport boilers, radiators, water treatment systems and fire-fighting equipment into the Strip.
The location for the hospital in question is the site of the former Jewish settlement of Netzarim in central Gaza, which was evacuated during the 2005 Israeli pullout from the area.
Israel imposed a blockade on Gaza Strip in June 2006, initially following the abduction of IDF soldier Gilad Shalit , who was released in October 2011.
The blockade was made more stringent in 2007, when Hamas took control of Gaza, and somewhat relaxed following international pressure in the wake of the 2010 flotilla incident.