UPDATE 3-U.S. Senate debates FDA regulation of tobacco

* Bill would give FDA oversight of cigarettes

* Democrats say they have enough votes for passage

* CBO: bill would boost deficit $900 mln through 2019

* Drug importation amendment expected (Adds expected amendments, senator's comments)

By Susan Heavey

WASHINGTON, June 2 (Reuters) - The U.S. Senate began debate Tuesday on whether to grant the Food and Drug Administration power to regulate tobacco products, a proposal that has divided the cigarette industry but won over health advocates.

A bill written by Democrats would let the FDA oversee the packaging, marketing and manufacturing of cigarettes and other tobacco products, which have been linked to cancer and other illnesses and kill 400,000 Americans each year.

In an 84-11 procedural vote, the Senate agreed to start debate, which could continue into next week. Democrats have said they have enough votes to approve the tobacco legislation but the margin could be slim.

Reaction from tobacco companies has been mixed. Altria Group Inc's (MO.N) Philip Morris unit, the nation's largest cigarette maker, supports the bill. But other companies, such as Reynolds American Inc's (RAI.N) R.J. Reynolds Tobacco unit and Lorillard Inc's (LO.N) Lorillard Tobacco Co, do not.