The visit came as Zalmay Khalilzad, who headed the US negotiating team in Doha across the table from Baradar, also visited Islamabad this week, though it was unclear if he was still in Pakistan Thursday.
The US Embassy in Islamabad has said only that Khalilzad was visiting the country "this week", while the State Department did not confirm his travel dates.
The Taliban's Doha-based spokesman, Suhail Shaheen, told AFP on Wednesday that the simultaneous visits to Pakistan were a "coincidence".
But when asked whether there was any possibility of the insurgents meeting Khalilzad, he replied: "Why not? It depends on the Americans."
The Taliban are still ready to sign the agreement which was hashed out between the two sides in Doha, he said.
"We stand for it. The Americans have backtracked and they will have to take the initiative."
Baradar was the most high-profile Afghan Taliban leader detained by Pakistan following the 9/11 attacks in 2001.
He was released from prison last October and appointed to head the insurgent's political office in a move seen as a tentative effort to aid the talks.
The Taliban have said that the Pakistan visit is the fourth leg of a tour that included Russia, China and Iran. A Taliban commander told AFP that Baradar and the 11 other militants will spend four days in Pakistan.