what is the best method to deal with a business competitor who
consistently prices the similar products much lower than market
threshold to gain market share?

If the company is a foreign producer that is selling its product in
the United States for a price less than its price in its home market
or at a price that is lower than the cost of production, or if a
foreign government is providing financial assistance to benefit its
production, then you can petition the United States International
Trade Commission and the US Department of Commerce.  They can issue an
anti-dumping duty order or countervailing duty order to offset the
dumping or subsidies.

"Trade Remedy Investigations" United States International Trade
Commission (2004) http://www.usitc.gov/trade_remedy/731_ad_701_cvd/index.htm

If the competitor is practicing predatory pricing, which is typically
defined as selling its product below cost over a sufficient period of
time to drive others from the marketplace, you can file a complaint
with the Antitrust Division of the Department of Justice and the
Federal Trade Commission.  There may also be state laws that you can
seek to have enforced.  These apply to domestic firms.

"Predatory Pricing and State Below-cost Sales Statutes in the United
States: And Analysis" by Terry Calvani, Government of Canada
http://cb-bc.gc.ca/epic/internet/incb-bc.nsf/en/ct01491e.html

If the competitor is merely practicing vigorous competition, then you
have a choice to make.  You can either seek to match their price,
which you will probably have to consider if the product is a
commodity.  In this case, you would have to seek to become a more
efficient producer in order to maintain your existing level of
profitability. However, anything you can do to make your product less
of a commodity by adding value added services to it will help you
maintain your pricing.  Furthermore, your competitor will have
difficulty matching you because of their low price.  Examples of
value-added services could be improved service levels, more rapid
delivery, free consultation on its use, financing, or anything else
that your customers would find of value that would make your product
attractive even at its higher price.

Sincerely,

Wonko

In Germany, you could get the monopolies commission to chase him if he
were selling under cost price ...