This photo illustration taken on March 26, 2018 shows the Grab and Uber booking application seen on a smart phone in Singapore.

Singapore's competition watchdog on Thursday proposed fines on Uber and Grab and said they may have to unwind their merger because of "substantially lessened competition" in the market.

Uber sold its Southeast Asia business to ride-hailing rival Grab in March. The move saw the -based company acquiring a 27.5 percent stake in Grab and Uber CEO joining the firm's board.

But the Competition and Consumer Commission of Singapore (CCCS) raised concerns about the merger, saying it has reduced competition and led to increased fares. The watchdog said that both parties did not notify the authorities of the merger despite anticipating that there could be some anti-competitive issues.

The CCCS said that the merger means that the barriers to entry for new entrants are high and that it could lead to less innovation and a lower quality of product. As a result, Uber and Grab may be fined and the transaction could be unwound.

"CCCS may require the parties to unwind the transaction unless the aforesaid public consultation confirms that any of the proposed remedies, or any further remedies, are sufficient to address the identified competition concerns, and are implementable in practice," the watchdog said in a statement.

Some of these remedies include requiring Uber to sell Lion City Rentals, its car rental subsidiary in Singapore, to another competitor and forcing Grab to remove any exclusivity it has with other taxi firms. For example, some drivers for other taxi firms can only accept bookings from Grab and not from any competitors.

Uber and Grab have 15 working days to make their proposals for remedies to the CCCS.

Grab said it disagreed with the watchdog's analysis and would appeal the decision.

"The CCCS appears to have taken a very narrow approach in defining competition. While we are one of the most visible players in transport, we are not the only player in the market. CCCS has not taken into account the dynamic developments and intense competition going on over the past few months, from both new and incumbent taxi and ride-hailing players," a Grab spokesperson told CNBC by email Thursday.

"Even though not required by the law, we had informed the CCCS that we were making a voluntary notification, as well as proactively engaged with the CCCS before the transaction was signed. We conducted the acquisition legally and in full compliance with Singapore’s applicable competition laws."

Grab said that it "fully co-operated" with the authorities during the review and called the CCCS' remedies "overreaching" and against Singapore's "pro-innovation" economy.