"We consider that as long as this attack is not solved in a way that satisfies Fenerbahce and public opinion, a suspension of the championship is inevitable," the Istanbul club said on its website.
"Blood ran and football was silenced. Finding and punishing the culprits is of vital importance for Fenerbahce."
The bus came under gunfire on Sunday (AEDT) as the Turkish Super Lig leader passed through the northeastern town of Trabzon after its away game in nearby Rize, where its beat Rizespor 5-1.
No players were hurt, but the driver was wounded in the face, said the club's vice-president Mahmut Uslu, accusing the still unidentified assailants of having tried to "crash the bus and kill the players".
"A black mark for Turkish football," the daily Hurriyet newspaper reported.
Pictures of the bus showed a damaged windshield on the driver's side.
Trabzon governor Abdil Celil Oz confirmed the gun attack on the bus and said the driver's life was not in danger.
"At first, we thought stones had been thrown at the bus but police investigators at the scene have concluded it was an armed attack," he told television station 360.
The governor revealed he received a phone call from President Recep Tayyip Erdogan, a supporter of the Istanbul club, asking him about the investigation into the attack.
It was a cowardly and inhuman attack," Sports Minister Cagatay Kilic said.
Media reports said the shots caused the driver to lose control of the vehicle but a team security official managed to slam on the brakes to prevent it plunging into a ravine.
The team had been on its way to Trabzon airport to catch a flight back to Istanbul and was later given an armed escort to the airport.
Kilic softened earlier opposition to the idea of suspending football matches, saying all options were being considered.
The Turkish Football Federation issued a statement condemning the incident in the strongest possible terms and called for the perpetrators to be brought to justice immediately.
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