NEW YORK (Reuters) - An activist investor who has been campaigning for change at Alere Inc (>> Alere Inc) sent the company a letter on Monday calling for the health diagnostics and services company to sell three of its businesses, which it believes can yield more than $3 billion in proceeds.

Coppersmith Capital Management, which holds a 5.8 percent stake in the company, has been pressuring the company to make changes since last month. The hedge fund has nominated a slate of three directors to Alere's board.

The hedge fund sent the letter days after Alere put its own slate of new nominees up for election to its board, replacing all four of the board members who were expected to stand for reelection this year.

Coppersmith said in the letter - which has been reviewed by Reuters - that Alere should exit non-core businesses including its health care management business, called Health Information Solutions; its consumer products joint venture with Procter & Gamble (>> The Procter & Gamble Company); and, possibly, its toxicology unit.

It said the proceeds, which it believes could total more than $3 billion, should be used to lower the company's debt. It said that cutting corporate overhead and spending could yield another $50 million to $100 million in yearly cost savings.

"Rather than embrace these common sense strategic changes, you have chosen to replace your 2013 incumbent nominees in what we consider to be a tactical effort to defeat an election challenge," Jerome Lande, managing partner of Coppersmith, wrote in the letter.

"While we fervently believe in adding fresh perspective to the board, the timing and manner of your nominations calls into question the sincerity of your stated motivation for effecting such change."

Alere has a $2.15 billion market value, but nearly $3.8 billion in long-term debt.

Coppersmith, founded by former partners of now-liquidated activist fund MMI Investments, has already said publicly that Alere should sell or close its struggling health management business, which it had built up through acquisitions worth $1.8 billion - with $1.4 billion of that amount already written off.

A representative for Coppersmith declined to comment.

Alere's toxicology business offers drug testing products and services to hospitals, clinics, law enforcement agencies and rehabilitation centers and helps them detect drug or alcohol abuse. Larger rivals Quest Diagnostics Inc (>> Quest Diagnostics Inc) and Laboratory Corporation of America Holdings (>> Laboratory Corp. of America Holdings) also make drug-testing products and services.

Alere itself toyed with the idea of selling the unit in the past. Chief Executive Ron Zwanziger said at the JPMorgan healthcare conference in January 2011 that the company had a "fair amount of debt" on the balance sheet and could opt to sell the toxicology business if needed to pay down debt.

Selling the profitable toxicology and the consumer products joint venture unit could trigger a sizeable tax. But Alere could offset the tax hit by selling the health management business first, to generate an "enormous" tax loss, Coppersmith said in the letter.

Waltham, Massachusetts-based Alere, which makes a range of diagnostic tools such as home pregnancy tests and fertility monitoring kits, expanded its disease management operations with the $900 million acquisition of Matria Healthcare in 2008.

The New York-based hedge fund, however, has argued that diagnostics and health management are different businesses, and is asking the company to reverse its acquisition strategy of the past several years.

(Reporting by Michael Erman and Soyoung Kim; Editing by Bernard Orr)

By Michael Erman and Soyoung Kim