The two incidents raised concern among authorities and prompted Governor Greg Abbott to call the incidents offensive and disturbing.
"Religious discrimination has no place in the State of Texas and I have faith that law enforcement spearheading this investigation will redouble their efforts to swiftly bring those responsible to justice," Abbott said in a statement on Monday.
In the most recent incident, the words "JEW" and "JEWS" were spray painted on a storage building at Congregation Agudas Achim, the largest conservative synagogue in the city.
Last week vandals spray-painted swastikas, the letters "KKK" and other racist slogans at Congregation Rodfei Sholom, the city's largest Orthodox synagogue, which is less than two miles away.
No arrests have been made in either case and both are being treated as hate crimes, police said."I am extremely disgusted and saddened at what happened at our synagogue this morning, especially considering what happened at Rodfei Sholom last week," said Jeffrey Abraham, the senior rabbi at Agudas Achim.