Ozil and Gundogan, who are both of Turkish descent, were selected by Low in his provisional World Cup squad after being pictured at Turkey's London embassy alongside Erdogan ahead of the politician's meeting with UK prime minister Theresa May earlier this month.
Erdogan is seeking re-election in his homeland against a backdrop of pressure from human rights groups and exiled Turkish citizens, who have denounced the government's vast arrest of journalists, civil rights activists and political opponents.
The German Football Federation (DFB) criticised Ozil and Gundogan, who appeared alongside Everton and Turkey striker Cenk Tosun, for taking part in an "election campaign stunt" – an observation that was branded "unacceptable" by the Turkish Football Federation (TFF) .
Speaking at a news conference on Thursday after Germany convened at their Eppan training camp, Low confirmed he had discussed the matter with his players and felt it was time to draw a line under the episode.
"We've had a private discussion and both players have assured us that no political message was intended," he said.
"For me, it's no longer an issue within the team and the sporting aspects will now take over."
The other source of pre-tournament controversy around the Germany squad has been Bayern Munich striker Sandro Wagner reacting in outspoken fashion to his omission.
Uncapped Freiburg forward Nils Petersen was the beneficiary and now has a chance to make an impression before Low trims his group to 23 on June 4.
"I felt it was important to have three strikers at the training camp to see what fits together best," Low said.
"I'm keen to see how Nils Petersen adjusts to this level, but I back him to show his quality.
"I've already spoken about [Wagner] twice. I don't see why I should say anything else about it."
Low confirmed Bayern Munich defender Jerome Boateng will have tests on a thigh injury in Munich on Friday.
"Then we'll decide whether or not he can join us this weekend. I think he'll be able to train next week though."