* Antitrust watchdog fined Google $20.95 mln in February
* Google abusing dominance in online web search, watchdog said
* Indian matchmaking website to argue fine inadequate
* Google appeal says company not engaged in search bias: source (Releads, adds challenge to ruling by Google's opponent in case)
NEW DELHI/MUMBAI, April 10 (Reuters) - Google has appealed against a ruling by India's competition watchdog that found it guilty of "search bias", while the website that brought the case also challenged the outcome, complaining the online search giant had got off too lightly.
In February, the Competition Commission of India (CCI) fined Google 1.36 billion rupees ($21 million), saying it was also abusing its dominance by giving its own online airline flight search product an unfair advantage over rivals.
Google, the core unit of U.S. firm Alphabet Inc, said on Tuesday it had filed an appeal.
"We disagree with aspects of the CCI's decision, so we have filed an appeal and sought a stay on those findings," a Google spokesman told Reuters.
After the February ruling, Google had referred to the issues raised by the Commission as "narrow concerns". It noted the order indicated that on the majority of issues the CCI examined, Google's conduct complied with Indian competition laws.
However, a lawyer with knowledge of the matter said on Tuesday that Matrimony.com, the Indian matchmaking website that had filed the case against Google was dissatisfied with the outcome and had lodged its own appeal.
Matrimony.com, according to the lawyer, has appealed against both the size of the fine, which it says is too small, and the CCI's ruling that neither Google's specialised search design or its advertising service, AdWords, were breaking competition rules. Google did not comment on that development.
A CCI official called the watchdog's judgement "robust" and said it would defend its ruling at the National Company Law Appellate Tribunal (NCLAT).
"Google was found to be indulging in practices of search bias and by doing so, it causes harm to its competitors as well as to users," the CCI had said in its 190-page ruling.
Search bias refers to the propensity for a search engine to favour certain websites over others in response to user queries, due to biases in their search algorithms or other factors. This can unduly hurt businesses that often rely on search engines to draw customers to their portals.
The appeal filed by Matrimony.com will be the latest anti-trust headache for Google, which remains mired in similar cases elsewhere in the world.
Last year, the European Commission imposed a record 2.4 billion euro ($3 billion) fine on the company for favouring its shopping service and demoting rival offerings. Google has appealed against the verdict. (Additional reporting by Sankalp Phartiyal; Editing by Euan Rocha, Simon Cameron-Moore and Mark Potter)