Members of the Hazara minority community have refused to end their sit-in in Quetta against the killing of 11 coal miners in Pakistan's Balochistan province, while demanding justice over the carnage.
On Monday night, Rashid met a delegation of the Majlis-e-Wahdatul Muslimeen (MWM) political organisation, who are leading the sit-in.
But the protesters refused to end their sit-in until Prime Minister Imran Khan visited them.
Addressing reporters after the meeting, Rashid said that he had asked the MWM to form a five-to-seven-member committee to meet the Prime Minister in Islamabad.
"I will arrange the meeting within two-three days," he was quoted as saying.
The Minister also announced a 2.5 million PKR compensation to the victims' families.
On Sunday, the 11 coal miners were kidnapped and killed by unidentified armed men in Machh, an area under serious security threat.
According to the police, the attackers abducted the miners and took them to the nearby hills where they were fired at and seriously injured.
The attack has been claimed by the Islamic State terror attack.