Dave Walls, the corporate giant's operations' director for its north west Europe operations, said he was sorry for the disruption to the local community.
He told an open meeting at Carloway that he was focused on the safe removal of the 17,000 tonne drilling platform.
At present there is no evidence of any pollution or damage to aquaculture.
"Should that transpire Transocean would meet its obligations. We will make right any damage. We are committed to do the right thing. We will stand by the community," said the oil firm chief.
Mr Walls also responded to accusations from Carloway Community Association that the company and other groups involved in the aftermath of the incident had ignored the community until now.
Seeking feedback on what was happening, the association -
The Transocean boss apologised. He said: "I hope you will us the opportunity to make it right. I can assure you we will stand by our commitments, our obligations. It was not intentional if you feel you were disregarded.
Mr Walls highlighted he was "personally extremely sorry" for the inconvenience to the local community.
He expressed gratitude for the support and the friendship of villagers and the wider community.
Transocean apologises for grounded oil rig
19 August 2016
Transocean has apologised for the grounded oil rig at Lewis.
Dave Walls of Transocean
The salvage operation plans to tow the structure off the rocks and to shelter without harm to people or the environment.
A date for the tow off has not been set as the condition of 25 damaged tanks has to be fully assessed.
Mr Walls said: “We are not there yet.
Once ready to refloat, a suitable weather window with "no wind and the right tide" is required, he said.
"We only get one opportunity. We will do it once and we will do it right. What we won't do is make it worse," he added.
Transocean will leave Dalmore beach in the condition it found it, he said.
"You won't know we've been here."
It will commission a "clean sweep of the seabed" to ensure there is no debris or pollution left behind.
Around 120 people attended the meeting in Carloway