Gotabhaya Rajapaksa said the count proves the number of people killed as a result of government action was “far too small” to constitute war crimes.
In April, a UN-backed report said tens of thousands may have died and pointed to evidence of army bombardment.
The government has rejected such claims and calls for an international probe.
In May 2009, the army defeated Tamil Tiger rebels fighting for a separate homeland in the north and east of Sri Lanka, after almost 26 years of civil war.
Much of the controversy surrounding the conduct of the army and the rebels centres on what happened during the closing stages of that war, when tens of thousands of civilians were hemmed into a narrow strip of land in the north of the country caught between government and rebel fighting.
For two years, the government maintained that no civilians died as a result of military action during the final stages of the conflict. But correspondents say that it has recently softened its stance on this line.
On Thursday, for the first time the defence secretary also acknowledged that a small number of soldiers may be responsible for some crimes.
But Mr Rajapaksa rejected any claims that civilians may have died in great numbers.
Analysts say that while the census of civilian deaths is the first time that the government has attempted to address the issue, it is unclear exactly how such a count has been conducted and how cause of death is being ascertained.
Human rights groups say that the Lessons Learnt and Reconciliation Commission (LLRC) is deeply flawed and has provided no accountability for atrocities the government is alleged to have committed during the war. The government insists the commission will provide justice.