The Republican nominee has singled Tur out at rallies before. He blasted her "dishonest" reporting at a December rally, prompting the Secret Service to escort her out after the event ended.
CNN's Wolf Blizter asked Conway about the incident on Wednesday. He said that Conway has spoken to Trump about calling out reporters before and asked how that conversation with Trump went.
Conway said that the conversation was "productive" and noted that she spoke with NBC News on Wednesday. She then said that Trump was not asking his supporters to go after Tur.
"We want fair coverage, and we want to be safe at our rallies. I don’t appreciate a lot of threats I get either from people who I guess are worried that we may actually win this thing. Lot of folks out there who should tamp it down but in the case of —I’m glad that you played the entire clip. Because Donald Trump, he’s not asking people to be mean to her. He’s not asking people to do anything, God forbid," she said.
Blizter then asked Conway if Trump calling one one reporter makes her "uncomfortable."
"I would always urge our supporters at these rallies and elsewhere, Wolf, to be civil and to be respectful to each other," Conway replied.
Then, when asked about the incident on "Morning Joe," Conway refused to say very much.
MSNBC's Willie Geist asked Conway, "Why is he calling people out by name in the back of the room?"
"He obviously didn't mean it in any malicious way. You heard what he said," Conway responded. "But I have spoken to NBC News about that issue, and I'll leave it there."
"Would you like to shed any light on it?" Geist then asked.
"No, sorry," Conway responded, before telling co-host Mika Brzezinksi that she could call her later. This prompted Geist to ask Conway why she would not talk about it on television.
In response, Conway began complaining that "the media" wants Clinton to win and that Americans don't want to be told how to think or act. When asked how that connected to Tur, Conway said it didn't.
After Conway complained more about media coverage of the presidential election, Geist asked her once more if she thinks Trump should have called out a reporter by name.
"I always prefer when he talks about institutions generally. And I had an exchange with Katy last night, and I’ve been in touch with NBC News," she replied.
Watch the "Morning Joe" interview via MSNBC. The conversation turns to Trump singling out Tur at the 10:15 mark.