However, the infrastructure major also insisted that it was keen to complete the ambitious project, saying that exchange of such letters is a "common practice" between any two parties.
When asked if L&T offers to hand over the project to the government, its chief executive and managing director V B Gadgil said, "In case the issues do not get settled."
"That (to quit) is one solution we have told them in case both of us are not able to resolve," he said but later added, "But that is only a gesture. Now there is a contact also."
Gadgil further said that writing such letters has been a common practice.
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"All such letters are very common between parties. These are contractual letters written by one party to the other party. Both the parties have right to reply and get the issues resolved. There are number of possible ways to resolve issues in any contract," Gadgil said.
"I reiterate my stand that we have no official communication of realignment except for stopping of work at some parts. Beyond that we are not sure...," Gadgil said.
The chief minister earlier in the day held multiple meetings with senior officials after a section of press reported that L&T offered to quit the project over a number of reasons.
Terming the media reports as a deliberate attempt to show the project in a poor light, a statement from the CM's Office said the correspondence between the L&T and the government is a routine thing.