Modi told Dhami that the Centre is providing all equipment necessary and resources required for the safe evacuation.
After not being able to rescue the workers for a week, the authorities on Sunday came up with a plan to drill operations from all three sides.
The tunnel on the Brahmakal-Yamunotri National Highway in Uttarakhand's Uttarkashi collapsed nine days ago.
The National Disaster Response Force (NDRF), State Disaster Relief Force (SDRF) and police are conducting the rescue operations.
A narrow opening was earlier made to insert an oxygen pipe in the tunnel and help the trapped labourers.
No casualties have been reported so far.